SUNIL Chopra_Meindl_SCM

188 Chapter 7 • Demand Forecasting in a Supply Chain Adaptive Forecasting In adaptive forecasting, the estimates of level, trend, and seasonality are updated after each demand observation. The main advantage of adaptive forecasting is that estimates incorporate all new data that are observed. We now discuss a basic framework and several methods that can be used for this type of forecast. The framework is provided in the most general setting, when the systematic component of demand data contains a level, a trend, and a seasonal factor. The framework we present is for the case in which the systematic component has the mixed form. It can, however, easily be modified for the other two cases. The framework can also be specialized for the case in which the systematic component contains no seasonality or trend. We assume that we have a set of historical data for n periods and that demand is seasonal with periodicity p. Given quarterly data, wherein the pattern repeats itself every year, we have a periodicity of p ϭ 4. We begin by defining a few terms: Lt ϭ estimate of level at the end of Period t Tt ϭ estimate of trend at the end of Period t St ϭ estimate of seasonal factor for Period t Ft ϭ forecast of demand for Period t (made in Period t Ϫ 1 or earlier) Dtϭ actual demand observed in Period t Et ϭ Ft – Dt ϭ forecast error in Period t In adaptive methods, the forecast for Period t ϩ l in Period t uses the estimate of level and trend in Period t (Lt and Tt respectively) and is given as Ft + l = 1Lt + lTt2St + l (7.7) The four steps in the adaptive forecasting framework are as follows: 1. Initialize: Compute initial estimates of the level (L0), trend (T0), and seasonal factors (S1,..., Sp) from the given data. This is done exactly as in the static forecasting method discussed earlier in the chapter with L0 ϭ L and T0 ϭ T. 2. Forecast: Given the estimates in Period t, forecast demand for Period t ϩ 1 using Equation 7.7. Our first forecast is for Period 1 and is made with the estimates of level, trend, and seasonal factor at Period 0. 3. Estimate error: Record the actual demand Dt+1 for Period t ϩ 1 and compute the error Et+1 in the forecast for Period t ϩ 1 as the difference between the forecast and the actual demand. The error for Period t ϩ 1 is stated as Et + 1 = Ft + 1 - Dt + 1 (7.8) 4. Modify estimates: Modify the estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Etϩ1 in the forecast. It is desirable that the modification be such that if the demand is lower than forecast, the estimates are revised downward, whereas if the demand is higher than forecast, the estimates are revised upward. The revised estimates in Period t ϩ 1 are then used to make a forecast for Period t ϩ 2, and Steps 2, 3, and 4 are repeated until all historical data up to Period n have been covered. The estimates at Period n are then used to forecast future demand. We now discuss various adaptive forecasting methods. The method that is most appropriate depends on the characteristic of demand and the composition of the systematic component of demand. In each case, we assume the period under consideration to be t. MOVING AVERAGE The moving average method is used when demand has no observable trend or seasonality. In this case, Systematic component of demand = level

Chapter 7 • Demand Forecasting in a Supply Chain 189 In this method, the level in Period t is estimated as the average demand over the most recent N periods. This represents an N-period moving average and is evaluated as follows: Lt = 1Dt + Dt - 1 + Á + Dt - N + 12/N (7.9) The current forecast for all future periods is the same and is based on the current estimate of level. The forecast is stated as Ft + 1 = Lt and Ft + n = Lt (7.10) After observing the demand for Period t ϩ 1, we revise the estimates as follows: Lt + 1 = 1Dt + 1 + Dt + Á + Dt - N + 22/N, Ft + 2 = Lt + 1 To compute the new moving average, we simply add the latest observation and drop the oldest one. The revised moving average serves as the next forecast. The moving average corresponds to giving the last N periods of data equal weight when forecasting and ignoring all data older than this new moving average. As we increase N, the moving average becomes less responsive to the most recently observed demand. We illustrate the use of the moving average in Example 7-1. EXAMPLE 7-1 Moving Average A supermarket has experienced weekly demand of milk of D1 ϭ 120, D2 ϭ127, D3 ϭ114, and D4 ϭ122 gallons over the past four weeks. Forecast demand for Period 5 using a four-period moving average. What is the forecast error if demand in Period 5 turns out to be 125 gallons? Analysis: We make the forecast for Period 5 at the end of Period 4. Thus, assume the current period to be t ϭ 4. Our first objective is to estimate the level in Period 4. Using Equation 7.9, with N ϭ 4, we obtain L4 = 1D4 + D3 + D2 + D12/4 = 1122 + 114 + 127 + 1202/4 = 120.75 The forecast of demand for Period 5, using Equation 7.10, is expressed as F5 = L4 = 120.75 gallons As demand in Period 5, D5, is 125 gallons, we have a forecast error for Period 5 of E5 = F5 - D5 = 125 - 120.75 = 4.25 After observing demand in Period 5, the revised estimate of level for Period 5 is given by L5 = 1D5 + D4 + D3 + D22/4 = 1125 + 122 + 114 + 1272/4 = 122 SIMPLE EXPONENTIAL SMOOTHING The simple exponential smoothing method is appropriate when demand has no observable trend or seasonality. In this case, Systematic component of demand = level The initial estimate of level, L0, is taken to be the average of all historical data because demand has been assumed to have no observable trend or seasonality. Given demand data for Periods 1 through n, we have the following: L0 = 1n a Di (7.11) n i=1 The current forecast for all future periods is equal to the current estimate of level and is given as Ft + 1 = Lt and Ft + n = Lt (7.12)

190 Chapter 7 • Demand Forecasting in a Supply Chain After observing the demand, Dtϩ1, for Period t ϩ 1, we revise the estimate of the level as follows: Lt+1 = aDt+1 + 11 - a2Lt (7.13) where a is a smoothing constant for the level, 0 6 a 6 1. The revised value of the level is a weighted average of the observed value of the level (Dt+1) in Period t ϩ 1 and the old estimate of the level (Lt) in Period t. Using Equation 7.13, we can express the level in a given period as a function of the current demand and the level in the previous period. We can thus rewrite Equation 7.13 as t-1 Lt+1 = a a11 - a2nDt+1-n + 11 - a2tD1 n=0 The current estimate of the level is a weighted average of all of the past observations of demand, with recent observations weighted higher than older observations. A higher value of a corresponds to a forecast that is more responsive to recent observations, whereas a lower value of a represents a more stable forecast that is less responsive to recent observations. We illustrate the use of exponential smoothing in Example 7-2. EXAMPLE 7-2 Simple Exponential Smoothing Consider the supermarket in Example 7-1, in which weekly demand for milk has been D1 ϭ 120, D2 ϭ127, D3 ϭ114, and D4 ϭ122 gallons over the past four weeks. Forecast demand for Period 5 using simple exponential smoothing with a = 0.1. Analysis: In this case, we have demand data for n ϭ 4 periods. Using Equation 7.11, the initial estimate of level is expressed by 4 L0 = a Di/4 = 120.75 i=1 The forecast for Period 1 (using Equation 7.12) is thus given by F1 = L0 = 120.75 The observed demand for Period 1 is D1 ϭ 120. The forecast error for Period 1 is given by E1 = F1 - D1 = 120.75 - 120 = 0.75 With a = 0.1, the revised estimate of level for Period 1 using Equation 7.13 is given by L1 = aD1 + 11 - a2L0 = 0.1 * 120 + 0.9 * 120.75 = 120.68 Observe that the estimate of level for Period 1 is lower than for Period 0 because the demand in Period 1 is lower than the forecast for Period 1. We thus obtain F2 ϭ L1 ϭ 120.68. Given that D2 ϭ 127, we obtain L2 ϭ 0.1 ϫ 127 ϩ 0.9 ϫ 120.68 ϭ 121.31. This gives F3 ϭ L2 ϭ 121.31. Given that D3 ϭ 114, we obtain L3 ϭ 0.1 ϫ 114 ϩ 0.9 ϫ 121.31 ϭ 120.58. This gives F4 ϭ L3 ϭ 120.58. Given that D4 ϭ 122, we obtain L4 ϭ 0.1 ϫ 122 ϩ 0.9 ϫ 120.58 ϭ 120.72. This gives F5 ϭ L4 ϭ 120.72. TREND-CORRECTED EXPONENTIAL SMOOTHING (HOLT’S MODEL) The trend-corrected exponential smoothing (Holt’s model) method is appropriate when demand is assumed to have a level and a trend in the systematic component but no seasonality. In this case, we have Systematic component of demand = level + trend

Chapter 7 • Demand Forecasting in a Supply Chain 191 We obtain an initial estimate of level and trend by running a linear regression between demand Dt and time Period t of the form Dt = at + b In this case, running a linear regression between demand and time periods is appropriate because we have assumed that demand has a trend but no seasonality. The underlying relation- ship between demand and time is thus linear. The constant b measures the estimate of demand at Period t ϭ 0 and is our estimate of the initial level L0. The slope a measures the rate of change in demand per period and is our initial estimate of the trend T0. In Period t, given estimates of level Lt and trend Tt, the forecast for future periods is expressed as Ft + 1 = Lt + Tt and Ft + n = Lt + nTt (7.14) After observing demand for Period t, we revise the estimates for level and trend as follows: Lt+1 = aDt+1 + 11 - a21Lt + Tt2 (7.15) Tt+1 = b1Lt+1 - Lt2 + 11 - b2Tt (7.16) where a is a smoothing constant for the level, 0 6 a 6 1, and b is a smoothing constant for the trend, 0 6 b 6 1. Observe that in each of the two updates, the revised estimate (of level or trend) is a weighted average of the observed value and the old estimate. We illustrate the use of Holt’s model in Example 7-3. EXAMPLE 7-3 Holt’s Model An electronics manufacturer has seen demand for its latest MP3 player increase over the past six months. Observed demand (in thousands) has been D1 ϭ 8,415, D2 ϭ 8,732, D3 ϭ 9,014, D4 ϭ 9,808, D5 ϭ 10,413, and D6 ϭ 11,961. Forecast demand for Period 7 using trend-corrected exponential smoothing with a = 0.1, b = 0.2. Analysis: The first step is to obtain initial estimates of level and trend using linear regression. We first run a linear regression (using the Excel tool Data | Data Analysis | Regression) between demand and time periods. The estimate of initial level L0 is obtained as the intercept coefficient, and the trend T0 is obtained as the X variable coefficient (or the slope). For the MP3 player data, we obtain L0 = 7,367 and T0 = 673 The forecast for Period 1 (using Equation 7.14) is thus given by F1 = L0 + T0 = 7,367 + 673 = 8,040 The observed demand for Period 1 is D1 = 8,415. The error for Period 1 is thus given by E1 = F1 - D1 = 8,040 - 8,415 = - 375 With a = 0.1, b = 0.2, the revised estimate of level and trend for Period 1 using Equations 7.15 and 7.16 is given by L1 = aD1 + 11 - a21L0 + T02 = 0.1 * 8,415 + 0.9 * 8,040 = 8,078 T1 = b1L1 - L02 + 11 - b2T0 = 0.2 * 18,078 - 7,3672 + 0.8 * 673 = 681 Observe that the initial estimate for demand in Period 1 is too low. As a result, our updates have increased the estimate of level L1 for Period 1 from 8,040 to 8,078 and the

192 Chapter 7 • Demand Forecasting in a Supply Chain estimate of trend from 673 to 681. Using Equation 7.14, we thus obtain the following forecast for Period 2: F2 = L1 + T1 = 8,078 + 681 = 8,759 Continuing in this manner, we obtain L2 = 8,755, T2 = 680, L3 = 9,393, T3 = 672, L4 = 10,039, T4 = 666, L5 = 10,676, T5 = 661, L6 = 11,399, T6 = 673. This gives us a forecast for Period 7 of F7 = L6 + T6 = 11,399 + 673 = 12,072 TREND- AND SEASONALITY-CORRECTED EXPONENTIAL SMOOTHING (WINTER’S MODEL) This method is appropriate when the systematic component of demand has a level, a trend, and a seasonal factor. In this case we have Systematic component of demand = 1level + trend2 * seasonal factor Assume periodicity of demand to be p. To begin, we need initial estimates of level (L0), trend (T0), and seasonal factors (S1, . . . , Sp). We obtain these estimates using the procedure for static forecasting described earlier in the chapter. In Period t, given estimates of level, Lt, trend, Tt, and seasonal factors, St, . . ., St+p-1, the forecast for future periods is given by Ft + 1 = 1Lt + Tt2St + 1 and Ft + l = 1Lt + lTt2St + l (7.17) On observing demand for Period t + 1, we revise the estimates for level, trend, and seasonal factors as follows: Lt+1 = a1Dt+1/St+12 + 11 - a21Lt + Tt2 (7.18) Tt+1 = b1Lt+1 - Lt2 + 11 - b2Tt (7.19) St + p + 1 = g1Dt + 1/Lt + 12 + 11 - g2St + 1 (7.20) where a is a smoothing constant for the level, 0 6 a 6 1; b is a smoothing constant for the trend, 0 6 b 6 1; and g is a smoothing constant for the seasonal factor, 0 6 g 6 1. Observe that in each of the updates (level, trend, or seasonal factor), the revised estimate is a weighted average of the observed value and the old estimate. We illustrate the use of Winter’s model in Example 7-4. EXAMPLE 7-4 Winter’s Model Consider the Tahoe Salt demand data in Table 7-1. Forecast demand for Period 1 using trend-and seasonality-corrected exponential smoothing with a = 0.1, b = 0.2, g = 0.1. Analysis: We obtain the initial estimates of level, trend, and seasonal factors exactly as in the static case. They are expressed as follows: L0 = 18,439 T0 = 524 S1 = 0.47 S2 = 0.68 S3 = 1.17 S4 = 1.67 The forecast for Period 1 (using Equation 7.17) is thus given by F1 = 1L0 + T02S1 = 118,439 + 52420.47 = 8,913 The observed demand for Period 1 is D1 ϭ 8,000. The forecast error for Period 1 is thus given by E1 = F1 - D1 = 8,913 - 8,000 = 913

Chapter 7 • Demand Forecasting in a Supply Chain 193 With a = 0.1, b = 0.2, g = 0.1, the revised estimate of level and trend for Period 1 and seasonal factor for Period 5, using Equations 7.18, 7.19, and 7.20, is given by L1 = a1D1/S12 + 11 - a21L0 + T02 = 0.1 * 18,000/0.472 + 0.9 * 118,439 + 5242 = 18,769 T1 = b1L1 - L02 + 11 - b2T0 = 0.2 * 118,769 - 18,4392 + 0.8 * 524 = 485 S5 = g1D1/L12 + 11 - g2S1 = 0.118,000/18,7692 + 0.9 * 0.47 = 0.47 The forecast of demand for Period 2 (using Equation 7.17) is thus given by F2 = 1L1 + T12S2 = 118,769 + 48520.68 = 13,093 The forecasting methods we have discussed and the situations in which they are generally applicable are as follows: Forecasting Method Applicability Moving average No trend or seasonality Simple exponential smoothing No trend or seasonality Holt’s model Trend but no seasonality Winter’s model Trend and seasonality If Tahoe Salt uses an adaptive forecasting method for the sell-through data obtained from its retailers, Winter’s model is the best choice, because its demand experiences both a trend and seasonality. If we do not know that Tahoe Salt experiences both trend and seasonality, how can we find out? Forecast error helps identify instances in which the forecasting method being used is inappropriate. In the next section, we describe how a manager can estimate and use forecast error. 7.6 MEASURES OF FORECAST ERROR As mentioned earlier, every instance of demand has a random component. A good forecasting method should capture the systematic component of demand but not the random component. The random component manifests itself in the form of a forecast error. Forecast errors contain valuable information and must be analyzed carefully for two reasons: 1. Managers use error analysis to determine whether the current forecasting method is predicting the systematic component of demand accurately. For example, if a forecasting method consistently produces a positive error, the forecasting method is overestimating the systematic component and should be corrected. 2. All contingency plans must account for forecast error. Consider a mail-order company with two suppliers. The first is in the Far East and has a lead time of two months. The second is local and can fill orders with one week’s notice. The local supplier is more expensive than the Far East supplier. The mail-order company wants to contract a certain amount of contingency capacity with the local supplier to be used if the demand exceeds the quantity the Far East supplier provides. The decision regarding the quantity of local capacity to contract is closely linked to the size of the forecast error. As long as observed errors are within historical error estimates, firms can continue to use their current forecasting method. Finding an error that is well beyond historical estimates may indicate that the forecasting method in use is no longer appropriate or demand has fundamentally changed. If all of a firm’s forecasts tend to consistently over- or underestimate demand, this may be another signal that the firm should change its forecasting method.

194 Chapter 7 • Demand Forecasting in a Supply Chain As defined earlier, forecast error for Period t is given by Et, where the following holds: Et = Ft - Dt That is, the error in Period t is the difference between the forecast for Period t and the actual demand in Period t. It is important that a manager estimate the error of a forecast made at least as far in advance as the lead time required for the manager to take whatever action the forecast is to be used for. For example, if a forecast will be used to determine an order size and the supplier’s lead time is six months, a manager should estimate the error for a forecast made six months before demand arises. In a situation with a six-month lead time, there is no point in estimating errors for a forecast made one month in advance. One measure of forecast error is the mean squared error (MSE), where the following holds (the denominator in Equation 7.21 can also have n Ϫ 1 instead of n): MSEn = 1 n (7.21) n a Et2 t=1 The MSE can be related to the variance of the forecast error. In effect, we estimate that the random component of demand has a mean of 0 and a variance of MSE. The MSE penalizes large errors much more significantly than small errors because all errors are squared. Thus, if we select forecast methods by minimizing MSE, a method with a forecast error sequence of 10, 12, 9, and 9 will be preferred to a method with an error sequence of 1, 3, 2, and 20. Thus, it is a good idea to use the MSE to compare forecasting methods if the cost of a large error is much larger than the gains from very accurate forecasts. Using the MSE as a measure of error is appropriate when forecast error has a distribution that is symmetric about zero. Define the absolute deviation in Period t, At, to be the absolute value of the error in Period t; that is, At = ƒ Et ƒ Define the mean absolute deviation (MAD) to be the average of the absolute deviation over all periods, as expressed by MADn = 1n a At (7.22) n t=1 The MAD can be used to estimate the standard deviation of the random component assuming that the random component is normally distributed. In this case the standard deviation of the random component is s = 1.25 MAD (7.23) We then estimate that the mean of the random component is 0, and the standard deviation of the random component of demand is s. MAD is a better measure of error than MSE if the forecast error does not have a symmetric distribution. Even when the error distribution is symmetric, MAD is an appropriate choice when selecting forecasting methods if the cost of a forecast error is proportional to the size of the error. The mean absolute percentage error (MAPE) is the average absolute error as a percentage of demand and is given by n ` Et ` 100 Dt MAPEn = a (7.24) t=1 n The MAPE is a good measure of forecast error when the underlying forecast has significant seasonality and demand varies considerably from one period to the next. Consider a scenario where two methods are used to make quarterly forecasts for a product with seasonal demand that peaks in the third quarter. Method 1 returns forecast errors of 190, 200, 245, and 180;

Chapter 7 • Demand Forecasting in a Supply Chain 195 Method 2 returns forecast errors of 100, 120, 500, and 100 over four quarters. Method 1 has a lower MSE and MAD relative to Method 2 and would be preferred if either criterion was used. If demand is highly seasonal, however, and averages 1,000, 1,200, 4,800, and 1,100 in the four periods, Method 2 results in MAPE ϭ 9.9%, while Method 1 results in a much higher MAPE ϭ 14.3%. In this instance, it can be argued that Method 2 should be preferred to Method 1. When a forecast method stops reflecting the underlying demand pattern (e.g., if demand drops considerably as it did for the automotive industry in 2008/2009), the forecast errors are unlikely to be randomly distributed around 0. In general, one needs a method to track and control the forecasting method. One approach is to use the sum of forecast errors to evaluate the bias, where the following holds: n (7.25) biasn = a Et t=1 The bias will fluctuate around 0 if the error is truly random and not biased one way or the other. Ideally, if we plot all the errors, the slope of the best straight line passing through should be 0. The tracking signal (TS) is the ratio of the bias and the MAD and is given as TSt = biast (7.26) MADt If the TS at any period is outside the range ; 6, this is a signal that the forecast is biased and is either underforecasting (TS 6 - 6) or overforecasting (TS 7 + 6). This may happen because the forecasting method is flawed or the underlying demand pattern has shifted. One instance in which a large negative TS will result occurs when demand has a growth trend and the manager is using a forecasting method such as moving average. Because trend is not included, the average of historical demand is always lower than future demand. The negative TS detects that the forecasting method consistently underestimates demand and alerts the manager. The tracking signal may also get large when demand has suddenly dropped (as it did for many industries in 2009) or increased by a significant amount making historical data less relevant. If demand has suddenly dropped, it makes sense to increase the weight on current data relative to older data when making forecasts. McClain (1981) recommends the “declining alpha” method when using exponential smoothing where the smoothing constant starts large (to give greater weight to recent data) but then decreases over time. If we are aiming for a long-term smoothing constant of α ϭ 1– ρ, a declining alpha approach would be to start with α0 ϭ 1 and reset the smoothing constant as follows: at = r at - 1 = 1 - r + at - 1 1 - rt In the long term, the smoothing constant will converge to α ϭ 1Ϫ ρ with the forecasts becoming more stable over time. 7.7 SELECTING THE BEST SMOOTHING CONSTANT When using exponential smoothing, the value of the smoothing constant chosen has a direct impact on the sensitivity of the forecast to recent data. If a manager has a good sense of the underlying demand pattern, it is best to use a smoothing constant that is no larger than 0.2. In general, it is best to pick smoothing constants that minimize the error term that a manager is most comfortable with from among MSE, MAD, and MAPE. In the absence of a preference among error terms, it is best to pick smoothing constants that minimize the MSE. We illustrate the impact of picking smoothing constants that minimize different error measures using the 10-period demand data shown in cells B3:B12 of Figure 7-5. The initial level is estimated using Equation 7.11 and is shown in cell C2. The smoothing constant α is obtained using Solver by minimizing the mean squared error MSE (cell F13) at the end of the 10 periods

196 Chapter 7 • Demand Forecasting in a Supply Chain FIGURE 7-5 Selecting Smoothing Constant by Minimizing MSE as shown in Figure 7-5. The forecast shown in Figure 7-5 uses the resulting α ϭ 0.54 and gives MSE ϭ 2,460, MAD ϭ 42.5, and MAPE ϭ 2.1 percent. The smoothing constant can also be selected using Solver by minimizing the MAD or the MAPE at the end of 10 periods. In Figure 7-6, we show the results from minimizing MAD (cell G13). The forecasts and errors with the resulting α ϭ 0.32 are shown in Figure 7-6. In this case, the MSE increases to 2,570 (compared to 2,460 in Figure 7-5) while the MAD decreases to 39.2 (compared to 42.5 in Figure 7-5) and the MAPE decreases to 2.0 percent (compared to 2.1 percent in Figure 7-5). The major difference between the two forecasts is in Period 9 (the period with the largest error shown in cell D11), where minimizing MSE picks a smoothing constant that reduces large errors, while minimizing MAD picks a smoothing constant that gives equal weight to reducing all errors even if large errors get somewhat larger.

Chapter 7 • Demand Forecasting in a Supply Chain 197 FIGURE 7-6 Selecting Smoothing Constant by Minimizing MAD In general, it is not a good idea to use smoothing constants much larger than 0.2 for extended periods of time. A larger smoothing constant may be justified for a short period of time when demand is in transition. It should, however, generally be avoided for extended periods of time. 7.8 FORECASTING DEMAND AT TAHOE SALT Recall the Tahoe Salt example earlier in the chapter with the historical sell-through demand from its retailers shown in Table 7-1. The demand data are also shown in column B of Figure 7-7. Tahoe Salt is currently negotiating contracts with suppliers for the four quarters between the second quarter of Year 4 and the first quarter of Year 5. An important input into this negotiation is the forecast of demand that Tahoe Salt and its retailers are building collaboratively. They have assigned a team consisting of two sales managers from the retailers and the vice president of

198 Chapter 7 • Demand Forecasting in a Supply Chain Cell Cell Formula Equation Copied to C5 =Average(B2:B5) 7.9 C6:C13 D6 =C5 7.10 D7:D13 E6 =D6-B6 7.8 E7:E13 F6 =Abs(E6) F7:F13 G6 =Sumsq($E$6:E6)/(A6-4) 7.21 G7:G13 H6 =Sum($F$6:F6)/(A6-4) 7.22 H7:H13 I6 =100*(F6/B6) I7:I13 J6 =Average($I$6:I6) 7.24 J7:J13 K6 =Sum($E$6:E6)/ H6 7.26 K7:K13 FIGURE 7-7 Tahoe Salt Forecasts Using Four-Period Moving Average operations for Tahoe Salt to come up with this forecast. The forecasting team decides to apply each of the adaptive forecasting methods discussed in this chapter to the historical data. The goal is to select the most appropriate forecasting method and then use it to forecast demand for the next four quarters. The team decides to select the forecasting method based on the errors that result when each method is used on the 12 quarters of historical demand data. Demand in this case clearly has both a trend and seasonality in the systematic component. Thus, the team initially expects Winter’s model to produce the best forecast. Moving Average The forecasting team initially decides to test a four-period moving average for the forecasting. All calculations are shown in Figure 7-7 and are as discussed in the section on the moving-average method earlier in this chapter. The team uses Equation 7.9 to estimate level and Equation 7.10 to forecast demand. As indicated by column K in Figure 7-7, the TS is well within the ; 6 range, which indicates that the forecast using the four-period moving average does not contain any significant bias. It does, however, have a fairly large MAD12 of 9,719, with a MAPE12 of 49 percent. From Figure 7-7, observe that L12 = 24,500

Chapter 7 • Demand Forecasting in a Supply Chain 199 Thus, using a four-period moving average, the forecast for Periods 13 through 16 (using Equation 7.10) is given by F13 = F14 = F15 = F16 = L12 = 24,500 Given that MAD12 is 9,719, the estimate of standard deviation of forecast error, using a four-period moving average, is 1.25 * 9,719 = 12,148. In this case, the standard deviation of forecast error is fairly large relative to the size of the forecast. Simple Exponential Smoothing The forecasting team next uses a simple exponential smoothing approach with a = 0.1 to forecast demand. This method is also tested on the 12 quarters of historical data. Using Equation 7.11, the team estimates the initial level for Period 0 to be the average demand for Periods 1 through 12. The initial level is the average of the demand entries in cells B3 to B14 in Figure 7-8 and results in L0 = 22,083 Cell Cell Formula Equation Copied to C4:C14 C3 =0.1*B3+(1- 7.13 D4:D14 0.1)*C2 E4:E14 F4:F14 D3 =C2 7.12 G4:G14 E3 =D3-B3 7.8 H4:H14 F3 =Abs(E3) I4:I14 G3 =Sumsq($E$3:E3)/ 7.21 J4:J14 A3 K4:K14 H3 =Sum($G$3:G3)/A3 7.22 I3 =100*(F3/B3) J3 =Average($I$3:I3) 7.24 K3 =Sum($F$3:F3)/H3 7.26 FIGURE 7-8 Tahoe Salt Forecasts Using Simple Exponential Smoothing

200 Chapter 7 • Demand Forecasting in a Supply Chain The team then uses Equation 7.12 to forecast demand for the succeeding period. The estimate of level is updated each period using Equation 7.13. The results are shown in Figure 7-8. As indicated by the TS, which ranges from Ϫ1.38 to 2.15, the forecast using simple exponential smoothing with a = 0.1 does not indicate any significant bias. However, it has a fairly large MAD12 of 10,208, with a MAPE12 of 59 percent. From Figure 7-8, observe that L12 = 23,490 Thus, the forecast for the next four quarters (using Equation 7.12) is given by F13 = F14 = F15 = F16 = L12 = 23,490 In this case, MAD12 is 10,208 and MAPE12 is 59 percent. Thus, the estimate of standard deviation of forecast error using simple exponential smoothing is 1.25 * 10,208 = 12,761. In this case, the standard deviation of forecast error is fairly large relative to the size of the forecast. Trend-Corrected Exponential Smoothing (Holt’s Model) The team next investigates the use of Holt’s model. In this case, the systematic component of demand is given by Systematic component of demand = level + trend The team applies the methodology discussed earlier. As a first step, it estimates the level at Period 0 and the initial trend. As described in Example 7-3, this estimate is obtained by running a linear regression between demand, Dt, and time, Period t. From the regression of the available data, the team obtains the following: L0 = 12,015 and T0 = 1,549 The team now applies Holt’s model with a = 0.1 and b = 0.2 to obtain the forecasts for each of the 12 quarters for which demand data are available. They make the forecast using Equation 7.14, they update the level using Equation 7.15, and they update the trend using Equation 7.16. The results are shown in Figure 7-9. As indicated by a TS that ranges from Ϫ2.15 to 2.00, trend-corrected exponential smoothing with a = 0.1 and b = 0.2 does not seem to significantly over- or underforecast. However, the forecast has a fairly large MAD12 of 8,836, with a MAPE12 of 52 percent. From Figure 7-9, observe that L12 = 30,443 and T12 = 1,541 Thus, using Holt’s model (Equation 7.14), the forecast for the next four periods is given by the following:1 F13 = L12 + T12 = 30,443 + 1,541 = 31,984 F14 = L12 + 2T12 = 30,443 + 2 * 1,541 = 33,525 F15 = L12 + 3T12 = 30,443 + 3 * 1,541 = 35,066 F16 = L12 + 4T12 = 30,443 + 4 * 1,541 = 36,607 In this case, MAD12 ϭ 8,836. Thus, the estimate of standard deviation of forecast error using Holt’s model with a = 0.1 and b = 0.2 is 1.25 * 8,836 = 11,045. In this case, the standard deviation of forecast error relative to the size of the forecast is somewhat smaller than it was with the previous two methods. However, it is still fairly large. 1 As a result of rounding, calculations done with only significant digits shown in the text may yield a different result. This is the case throughout the book.

Chapter 7 • Demand Forecasting in a Supply Chain 201 Cell Cell Formula Equation Copied to C3 =0.1*B3+(1-0.1)*(C2+D2) 7.15 C4:C14 D3 =0.2(C3-C2)+(1-0.2)D2 7.16 D4:D14 E3 =C2+D2 7.14 E4:E14 F3 =E3-B3 7.8 F4:F14 G3 =Abs(F3) G4:G14 H3 =Sumsq($F$3:F3)/A3 7.21 H4:H14 I3 =Sum($G$3:G3)/A3 7.22 I4:I14 J3 =100*(G3/B3) J4:J14 K3 =Average($J$3:J3) 7.24 K4:K14 L3 =Sum($F$3:F3)/I3 7.26 L4:L14 FIGURE 7-9 Trend-Corrected Exponential Smoothing Trend- and Seasonality-Corrected Exponential Smoothing (Winter’s Model) The team next investigates the use of Winter’s model to make the forecast. As a first step, it estimates the level and trend for Period 0, and seasonal factors for Periods 1 through p ϭ 4. To start, the demand is deseasonalized. Then, the team estimates initial level and trend by running a regression between deseasonalized demand and time. This information is used to estimate the seasonal factors. For the demand data in Figure 7-2, as discussed in Example 7-4, the team obtains the following: L0 = 18,439 T0 = 524 S1 = 0.47 S2 = 0.68 S3 = 1.17 S4 = 1.67 It then applies Winter’s model with a = 0.05, b = 0.1, g = 0.1 to obtain the forecasts. All calculations are shown in Figure 7-10. The team makes forecasts using Equation 7.17, updates the level using Equation 7.18, updates the trend using Equation 7.19, and updates seasonal factors using Equation 7.20. In this case, the MAD of 1,469 and MAPE of 8 percent are significantly lower than with any of the other methods. From Figure 7-10, observe that L12 = 24,791 T12 = 532 S13 = 0.47 S14 = 0.68 S15 = 1.17 S16 = 1.67

202 Chapter 7 • Demand Forecasting in a Supply Chain Cell Cell Formula Equation Copied to C3 =0.05*(B3/E3)+(1-0.05)*(C2+D2) 7.18 C4:C14 D3 =0.1*(C3-C2)+(1-0.1)*D2 7.19 D4:D14 E7 =0.1*(B3/C3)+(1-0.1)*E3 7.20 E8:E18 F3 =(C2+D2)*E3 7.17 F4:F18 G3 =F3-B3 7.8 G4:G14 H3 =Abs(G3) H4:H14 I3 =Sumsq($G$3:G3)/A3 7.21 I4:I14 J3 =Sum($H$3:H3)/A3 7.22 J4:J14 K3 =100*(H3/B3) K4:K14 L3 =Average($K$3:K3) 7.24 L4:L14 M3 =Sum($G$3:G3)/J3 7.26 M4:M14 FIGURE 7-10 Trend- and Seasonality-Corrected Exponential Smoothing Using Winter’s model (Equation 7.17), the forecast for the next four periods is F13 = 1L12 + T122S13 = 124,791 + 5322 * 0.47 = 11,940 F14 = 1L12 + 2T122S14 = 124,791 + 2 * 5322 * 0.68 = 17,579 F15 = 1L12 + 3T122S15 = 124,791 + 3 * 5322 * 1.17 = 30,930 F16 = 1L12 + 4T122S16 = 124,791 + 4 * 5322 * 1.67 = 44,928 In this case, MAD12 ϭ 1,469. Thus, the estimate of standard deviation of forecast error using Winter’s model with a = 0.05, b = 0.1, and g = 0.1 is 1.25 * 1,469 = 1,836. In this case, the standard deviation of forecast error relative to the demand forecast is much smaller than with the other methods. The team compiles the error estimates for the four forecasting methods as shown in Table 7-2. Based on the error information in Table 7-2, the forecasting team decides to use Winter’s model. It is not surprising that Winter’s model results in the most accurate forecast, because the

Chapter 7 • Demand Forecasting in a Supply Chain 203 Table 7-2 Error Estimates for Tahoe Salt Forecasting Forecasting Method MAD MAPE (%) TS Range Four-period moving average 9,719 49 Ϫ1.52 to 2.21 Simple exponential smoothing 10,208 59 Ϫ1.38 to 2.15 Holt’s model 52 Ϫ2.15 to 2.00 Winter’s model 8,836 8 Ϫ2.74 to 4.00 1,469 demand data have both a growth trend as well as seasonality. Using Winter’s model, the team forecasts the following demand for the coming four quarters: Second Quarter, Year 4: 11,940 Third Quarter, Year 4: 17,579 Fourth Quarter, Year 4: 30,930 First Quarter, Year 5: 44,928 The standard deviation of forecast error is 1,836. 7.9 THE ROLE OF IT IN FORECASTING There is a natural role for IT in forecasting, given the large amount of data involved, the frequency with which forecasting is performed, and the importance of getting the highest quality results possible. The forecasting module within a supply chain IT system, often called the demand planning module, is a core supply chain software product. Utilizing the capabilities of IT in forecasting has several important advantages. Commercial demand planning modules come with a variety of forecasting algorithms, which can be quite advanced and are sometimes proprietary. These methodologies often give a more accurate forecast than those produced through the use of a general package such as Excel. Most demand planning applications make it fairly easy to test the various forecasting algorithms against historical data to determine the one that provides the best fit to the observed demand patterns. The availability of a variety of forecasting options is important because different forecasting algorithms provide different levels of quality depending on the actual demand patterns. The IT system can thus be used to best determine forecasting methods not just for the firm overall, but also by product categories and markets. A good forecasting package provides forecasts across a wide range of products that are updated in real time by incorporating any new demand information. This helps firms respond quickly to changes in the marketplace and avoid the costs of a delayed reaction. Good demand planning modules link not only to customer orders but often directly to customer sales information as well, thus incorporating the most current data into the demand forecast. Much of the progress in areas such as collaborative planning is due to IT innovations that allow the exchange and incorporation of forecasts between enterprises. Finally, as the name demand planning suggests, these modules facilitate the shaping of demand. Good demand planning modules contain tools to perform what-if analysis regarding the impact of potential changes in prices on demand. These tools help analyze the impact of promotions on demand and can be used to determine the extent and timing of promotions. This link is discussed in greater detail in Chapter 9 under sales and operations planning. Keep in mind that none of these tools is foolproof. Forecasts are virtually always inaccurate. A good IT system should help track historical forecast errors so they can be incorporated into future decisions. A well-structured forecast, along with a measure of error, can significantly improve decision making. Even with all these sophisticated tools, sometimes it is

204 Chapter 7 • Demand Forecasting in a Supply Chain better to rely on human intuition in forecasting. One of the pitfalls of these IT tools is relying on them too much, which eliminates the human element in forecasting. Use the forecasts and the value they deliver, but remember that they cannot assess some of the more qualitative aspects about future demand that you may be able to do on your own. Forecasting modules are available from all the major supply chain software companies, including the ERP firms such as SAP and Oracle. A number of statistical analysis software firms, such as SAS and SPSS, have programs that can be used for forecasting. A detailed list of forecasting software vendors is reported in the OR/MS Today forecasting software survey, and a discussion of each vendor is available at http://www.lionhrtpub.com/orms/surveys/FSS/ fss-fr.html. 7.10 RISK MANAGEMENT IN FORECASTING The risks associated with forecast error must be considered when planning for the future. Errors in forecasting can cause significant misallocation of resources in inventory, facilities, transportation, sourcing, pricing, and even in information management. Forecast errors during network design may cause too many, too few, or the wrong type of facilities to be built. Plans are determined from forecasts so the actual inventory, production, transportation, sourcing, and pricing plans that a company produces and follows depend on accurate forecasting. Even on an operational level, forecasting plays a role in the actual day-to-day activities that are executed within a company. As one of the initial processes in each of these phases that affects many other processes, forecasting contains a significant amount of inherent risk. A wide range of factors can cause a forecast to be inaccurate, but a few occur so often that they deserve specific mention. Long lead times require forecasts to be made further in advance, thus decreasing the reliability of the forecast. Seasonality also tends to increase forecast error. Forecast errors increase when product life cycles are short, because there are few historical data to build on when producing a forecast. Firms with a few customers often experience lumpy demand that is harder to forecast than demand from many small customers, which tends to be smoother. Forecast quality suffers when it is based on orders placed by intermediaries in a supply chain rather than on end customer demand. This was particularly evident in the telecommunications sector in 2001, when manufacturer forecasts exceeded customer demand by a large amount. Without a view of end customer demand, a firm always has difficulty producing reliable forecasts. Two strategies used to mitigate forecast risk are increasing the responsiveness of the supply chain and utilizing opportunities for pooling of demand. Increased responsiveness allows the firm to reduce forecasting errors and thus decrease the associated risk. Zara and Seven-Eleven Japan have been successful by designing and operating responsive supply chains. Zara replenishes its stores several times a week while Seven-Eleven replenishes its stores several times a day. As a result, store managers in each case have to make short-term forecasts that are fairly accurate. Pooling, which we discuss in Chapter 12, attempts to smooth out lumpy demand by bringing together multiple sources of demand. Thus, Amazon has a lower forecast error than Barnes & Noble because it pools geographic demand into its warehouses. Improved responsiveness and pooling often come at a cost. Increased speed may require capacity investment, whereas pooling tends to increase transportation cost. To achieve the right balance between risk mitigation and cost, it is important to tailor the mitigation strategies. For instance, when dealing with a commodity for which shortfalls can easily be made up for by spot market purchases, spending large amounts to increase the responsiveness of the supply chain is not warranted. In contrast, for a product with a short life cycle (e.g., trendy clothes as is the case with Zara), investing in responsiveness may be worth the cost. Similarly, the benefit from pooling is likely to be large only when the underlying forecast error is high and the product value is high relative to transportation cost. An investment in pooling efforts may not be justified for

Chapter 7 • Demand Forecasting in a Supply Chain 205 products with small forecast errors. Blue Nile has been successful pooling high-value diamonds whose demand is difficult to forecast. In contrast, detergent, which is easy to forecast and has high transport costs relative to its value, is typically sold through decentralized retail stores. These ideas are discussed in greater detail in Chapters 4, 12, and 13. 7.11 FORECASTING IN PRACTICE Collaborate in building forecasts. Collaboration with your supply chain partners can often create a much more accurate forecast. It takes an investment of time and effort to build the relationships with your partners to begin sharing information and creating collaborative forecasts. However, the supply chain benefits of collaboration are often an order of magnitude greater than the cost (collaborative planning, forecasting, and replenishment are discussed in greater detail in Chapter 10). The reality today, however, is that most forecasts do not even account for all the information available across the different functions of a firm. As a result, firms should aim to put a sales and operations planning process in place (discussed in Chapter 9) that brings together the sales and operations functions when planning. Share only the data that truly provide value. The value of data depends on where one sits in the supply chain. A retailer finds point-of-sale data to be quite valuable in measuring the performance of its stores. However, a manufacturer selling to a distributor who in turn sells to retailers does not need all the point-of-sale detail. The manufacturer finds aggregate demand data to be quite valuable, with marginally more value coming from detailed point-of-sale data. Keeping the data shared to what is truly required decreases investment in IT and improves the chances of successful collaboration. Be sure to distinguish between demand and sales. Often, companies make the mistake of looking at historical sales and assuming that this is what the historical demand was. To get true demand, adjustments need to be made for unmet demand due to stockouts, competitor actions, pricing, and promotions. Failure to do so results in forecasts that do not represent the current reality. 7.12 SUMMARY OF LEARNING OBJECTIVES 1. Understand the role of forecasting for both an enterprise and a supply chain. Forecasting is a key driver of virtually every design and planning decision made in both an enterprise and a supply chain. Enterprises have always forecasted demand and used it to make decisions. A relatively recent phenomenon, however, is to create collaborative forecasts for an entire supply chain and use these as the basis for decisions. Collaborative forecasting greatly increases the accuracy of forecasts and allows the supply chain to maximize its performance. Without collaboration, supply chain stages farther from demand will likely have poor forecasts that will lead to supply chain inefficiencies and a lack of responsiveness. 2. Identify the components of a demand forecast. Demand consists of a systematic and a random component. The systematic component measures the expected value of demand. The random component measures fluctuations in demand from the expected value. The systematic component consists of level, trend, and seasonality. Level measures the current deseasonalized demand. Trend measures the current rate of growth or decline in demand. Seasonality indicates predictable seasonal fluctuations in demand. 3. Forecast demand in a supply chain given historical demand data using time-series methodologies. Time-series methods for forecasting are categorized as static or adaptive. In static methods, the estimates of parameters and demand patterns are not updated as new demand is observed. Static methods include regression. In adaptive methods, the estimates are

206 Chapter 7 • Demand Forecasting in a Supply Chain updated each time a new demand is observed. Adaptive methods include moving averages, simple exponential smoothing, Holt’s model, and Winter’s model. Moving averages and simple exponential smoothing are best used when demand displays no trend or seasonality. Holt’s model is best when demand displays a trend but no seasonality. Winter’s model is appropriate when demand displays both trend and seasonality. 4. Analyze demand forecasts to estimate forecast error. Forecast error measures the random component of demand. This measure is important because it reveals how inaccurate a forecast is likely to be and what contingencies a firm may have to plan for. The MSE, MAD, and MAPE are used to estimate the size of the forecast error. The bias and TS are used to estimate if the forecast consistently over- or underforecasts or if demand has deviated significantly from historical norms. Discussion Questions 1. What role does forecasting play in the supply chain of a 6. Give examples of products that display seasonality of build-to-order manufacturer such as Dell? demand. 2. How could Dell use collaborative forecasting with its 7. What is the problem if a manager uses last year’s sales data suppliers to improve its supply chain? instead of last year’s demand to forecast demand for the coming year? 3. What role does forecasting play in the supply chain of a mail-order firm such as L.L.Bean? 8. How do static and adaptive forecasting methods differ? 9. What information do the MSE, MAD, and MAPE provide to a 4. What systematic and random components would you expect in demand for chocolates? manager? How can the manager use this information? 10. What information do the bias and TS provide to a manager? 5. Why should a manager be suspicious if a forecaster claims to forecast historical demand without any forecast error? How can the manager use this information? Exercises the static method for forecasting. Evaluate the bias, TS, MAD, MAPE, and MSE. Evaluate the quality of the forecast. 1. Consider monthly demand for the ABC Corporation as shown in Table 7-3. Forecast the monthly demand for Year 6 using Table 7-3 Monthly Demand for ABC Corporation Sales Year 1 Year 2 Year 3 Year 4 Year 5 January 2,000 3,000 2,000 5,000 5,000 February 3,000 4,000 5,000 4,000 2,000 March 3,000 3,000 5,000 4,000 3,000 April 3,000 5,000 3,000 2,000 2,000 May 4,000 5,000 4,000 5,000 7,000 June 6,000 8,000 6,000 7,000 6,000 July 7,000 3,000 7,000 10,000 8,000 August 6,000 8,000 10,000 14,000 10,000 September 10,000 12,000 15,000 16,000 20,000 October 12,000 12,000 15,000 16,000 20,000 November 14,000 16,000 18,000 20,000 22,000 December 8,000 10,000 8,000 12,000 8,000 Total 78,000 89,000 98,000 115,000 113,000

2. Weekly demand at Hot Pizza are as follows: Chapter 7 • Demand Forecasting in a Supply Chain 207 Week Demand ($) 4. Consider monthly demand for the ABC Corporation as shown in Table 7-3. Forecast the monthly demand for Year 6 using 1 108 moving average, simple exponential smoothing, Holt’s model, 2 116 and Winter’s model. In each case, evaluate the bias, TS, 3 118 MAD, MAPE, and MSE. Which forecasting method do you 4 124 prefer? Why? 5 6 96 5. For the Hot Pizza data in Exercise 2, compare the performance 7 119 of simple exponential smoothing with a = 0.1 and a = 0.9. 8 What difference in forecasts do you observe? Which of the two 9 96 smoothing constants do you prefer? 10 102 11 112 6. Monthly demand at A&D Electronics for flat screen TVs are 12 102 as follows: 92 Month Demand (units) 91 1 1,00 Estimate demand for the next four weeks using a four-week 2 1,113 moving average as well as simple exponential smoothing 3 1,271 with a = 0.1. Evaluate the MAD, MAPE, MSE, bias, and TS 4 1,445 in each case. Which of the two methods do you prefer? Why? 5 1,558 3. Quarterly demand for flowers at a wholesaler are as shown. 6 1,648 Forecast quarterly demand for year 5 using simple exponen- 7 1,724 tial smoothing with a = 0.1 as well as Holt’s model with 8 1,850 a = 0.1 and b = 0.1. Which of the two methods do you 9 1,864 prefer? Why? 10 2,076 11 2,167 Year Quarter Demand (’000$) 12 2,191 1 I 98 Estimate demand for the next two weeks using simple 2 II 106 exponential smoothing with a = 0.3 and Holt’s model with III 109 a = 0.05 and b = 0.1. For the simple exponential smoothing 3 IV 133 model, use the level at Period 0 to be L0 = 1,659 (the average I 130 demand over the 12 months). For Holt’s model, use level at 4 II 116 III 133 Period 0 to be L0 = 948 and the trend in Period 0 to be IV 116 T0 = 109 (both are obtained through regression). Evaluate the I 138 MAD, MAPE, MSE, bias, and TS in each case. Which of II 130 III 147 the two methods do you prefer? Why? IV 141 I 144 7. Using the A&D Electronics data in Exercise 6, repeat Holt’s II 142 model with a = 0.5 and b = 0.5. Compare the performance of III 165 Holt’s model with a = 0.05 and b = 0.1. Which combination IV 173 of smoothing constants do you prefer? Why?

208 Chapter 7 • Demand Forecasting in a Supply Chain Bibliography Bernstein, Peter L., and Theodore H. Silbert. “Are Economic Gilliland, Michael. “Is Forecasting a Waste of Time?” Supply Forecasters Worth Listening To?” Harvard Business Review Chain Management Review (July–August 2002): 16–23. (September–October 1984): 2–8. McClain, John O. “Restarting a Forecasting System When Bowerman, Bruce L., and Richard T. O’Connell. Forecasting and Demand Suddenly Changes.” Journal of Operations Time Series: An Applied Approach, 3d ed. Belmont, CA: Management (October 1981): 53–61. Duxbury, 1993. Makridakis, S., A. Andersen, R. Carbone, R. Fildes, M. Hibon, Box, George E. P., and Gwilym M. Jenkins. Time Series Analysis: R. Lewandowski, J. Newton, E. Parzen, and R. Winkler. “The Forecasting and Control. Oakland, CA: Holden-Day, 1976. Accuracy of Extrapolation (Time Series) Methods: Results of a Forecasting Competition.” Journal of Forecasting (April–June Brown, Robert G. Statistical Forecasting for Inventory Control. 1982): 111–153. New York: McGraw-Hill, 1959. Makridakis, Spyros, and Steven C. Wheelwright. Forecasting Chambers, John C., Satinder K. Mullick, and Donald D. Smith. Methods for Management. New York: Wiley, 1989. “How to Choose the Right Forecasting Technique.” Harvard Business Review (July–August 1971): 45–74. Yurkiewicz, Jack. “Forecasting: What Can You Predict for Me?” ORMS Today (June 2010): 36–39. Software survey Forecasting with Regression Analysis. Cambridge, MA: Harvard available at http://www.lionhrtpub.com/orms/surveys/FSS/ Business School Note #9–894–007, 1994. fss-fr.html. Georgoff, David M., and Robert G. Murdick. “Manager’s Guide to Forecasting.” Harvard Business Review (January–February 1986): 2–9. CASE STUDY Specialty Packaging Corporation, Part A Julie Williams had a lot on her mind when she left the SPC conference room at Specialty Packaging Corporation (SPC). Her divisional manager had informed her that she SPC turns polystyrene resin into recyclable/disposable would be assigned to a team consisting of SPC’s marketing containers for the food industry. Polystyrene is pur- vice president and staff members from their key chased as a commodity in the form of resin pellets. The customers. The goal of this team was to improve supply resin is unloaded from bulk rail containers or overland chain performance, as SPC had been unable to meet trailers into storage silos. Making the food containers is a demand effectively over the previous several years. This two-step process. First, resin is conveyed to an extruder, often left SPC’s customers scrambling to meet new client which converts it into a polystyrene sheet that is wound demands. Julie had little contact with SPC’s customers and into rolls. The plastic comes in two forms—clear and wondered how she would add value to this process. She black. The rolls are either used immediately to make was told by her division manager that the team’s first task containers or are put into storage. Second, the rolls are was to establish a collaborative forecast using data from loaded onto thermoforming presses, which form the both SPC and its customers. This forecast would serve as sheet into containers and trim the containers from the basis for improving the firm’s performance, as the sheet. The two manufacturing steps are shown in managers could use this more accurate forecast for their Figure 7-11. production planning. Improved forecasts would allow SPC to improve delivery performance. Over the past five years, the plastic packaging business has grown steadily. Demand for containers Step 1 Step 2 Resin Extruder Roll Thermo- Storage Storage forming Press FIGURE 7-11 Manufacturing Process at SPC

Chapter 7 • Demand Forecasting in a Supply Chain 209 made from clear plastic comes from grocery stores, never have known this information, as the company did bakeries, and restaurants. Caterers and grocery stores not keep track of lost orders. use the black plastic trays as packaging and serving trays. Demand for clear plastic containers peaks in the Forecasting summer months, whereas demand for black plastic containers peaks in the fall. Capacity on the extruders is As a first step in the team’s decision making, it wants to not sufficient to cover demand for sheets during the peak forecast quarterly demand for each of the two types of seasons. As a result, the plant is forced to build inventory containers for the years 2010 to 2012. Based on histori- of each type of sheet in anticipation of future demand. cal trends, demand is expected to continue to grow until Table 7-4 and Figure 7-12 display historical quarterly 2012, after which it is expected to plateau. Julie must demand for each of the two types of containers (clear select the appropriate forecasting method and estimate and black). The team modified SPC’s sales data by the likely forecast error. Which method should she accounting for lost sales to obtain true demand data. choose? Why? Using the method selected, forecast Without the customers involved in this team, SPC would demand for the years 2010 to 2012. Table 7-4 Quarterly Historical Demand for Clear and Black Plastic Containers Year Quarter Black Plastic Clear Plastic Demand (’000 lb) Demand (’000 lb) 2005 I 2,250 3,200 2006 II 1,737 7,658 2007 III 2,412 4,420 2008 IV 7,269 2,384 2009 I 3,514 3,654 II 2,143 8,680 III 3,459 5,695 IV 7,056 1,953 I 4,120 4,742 II 2,766 13,673 III 2,556 6,640 IV 8,253 2,737 I 5,491 3,486 II 4,382 13,186 III 4,315 5,448 IV 12,035 3,485 I 5,648 7,728 II 3,696 16,591 III 4,843 8,236 IV 13,097 3,316 (continued)

210 Chapter 7 • Demand Forecasting in a Supply Chain (continued) 18000 Black Plastic Demand 16000 Clear Plastic Demand 14000 12000 Demand 10000 8000 6000 4000 2000 0 2006 2007 Year 2008 2009 2010 2005 FIGURE 7-12 Plot of Quarterly Demand for Clear and Black Plastic Containers

8 {{{ Aggregate Planning in a Supply Chain LEARNING OBJECTIVES After reading this chapter, you will be able to 1. Identify the decisions that are best solved by aggregate planning. 2. Understand the importance of aggregate planning as a supply chain activity. 3. Describe the information needed to produce an aggregate plan. 4. Explain the basic trade-offs to consider when creating an aggregate plan. 5. Formulate and solve basic aggregate planning problems using Microsoft Excel. In this chapter, we discuss how the aggregate planning methodology is used to make decisions about production, outsourcing, inventory, and backlogs in a supply chain. We identify the information required to produce an aggregate plan and outline the basic trade-offs that must be made to create an optimal aggregate plan. We also describe how to formulate and solve an aggregate planning problem using Microsoft Excel. 8.1 THE ROLE OF AGGREGATE PLANNING IN A SUPPLY CHAIN 211 Imagine a world in which manufacturing, transportation, warehousing, and even information capacity are all limitless and free. Imagine lead times of zero, allowing goods to be produced and delivered instantaneously. In this world, there would be no need to plan in anticipation of demand, because whenever a customer demands a product, the demand would be instantly satisfied. In this world, aggregate planning plays no role. In the real world, however, capacity has a cost, and lead times are often long. Therefore, companies must make decisions regarding capacity levels, production levels, outsourcing, and promotions well before demand is known. A company must anticipate demand and determine, in advance of that demand, how to meet it. Should a company invest in a plant with large capacity that is able to produce enough to satisfy demand even in the busiest months? Or should a company build a smaller plant but incur the costs of holding inventory built during slow periods in anticipa- tion of demand in later months? These are the types of questions that aggregate planning helps companies answer. Aggregate planning is a process by which a company determines planned levels of capacity, production, subcontracting, inventory, stockouts, and even pricing over a specified time horizon. The goal of aggregate planning is to build a plan that satisfies demand while maximizing profit. Aggregate planning, as the name suggests, solves problems involving aggregate decisions rather than stock-keeping unit (SKU)–level decisions.

212 Chapter 8 • Aggregate Planning in a Supply Chain For example, aggregate planning determines the total production level in a plant for a given month, but it does so without determining the quantity of each individual SKU that will be produced. This level of detail makes aggregate planning a useful tool for thinking about decisions with an intermediate time frame of between roughly 3 and 18 months. In this time frame, it is too early to determine production levels by SKU, but it is also generally too late to arrange for additional capacity. Therefore, aggregate planning answers the question: How should a firm best utilize the facilities that it currently has? To be effective, aggregate planning requires inputs from all stages of the supply chain, and its results have a tremendous impact on supply chain performance. As we saw in the previous chapter on forecasting, collaborative forecasts are created by multiple supply chain enterprises and are an important input for aggregate planning. In addition, many constraints that are key inputs to aggregate planning come from supply chain partners outside the enterprise. Without these inputs from both up and down the supply chain, aggregate planning cannot realize its full potential to create value. The output from aggregate planning is also of value to both upstream and downstream partners. Production plans for a firm define demand for suppliers and establish supply constraints for customers. This chapter is meant to create a foundation for using aggregate planning both solely within an enterprise as well as across the entire supply chain. The supply chain implications of aggregate planning will become even clearer in Chapter 9 in which we discuss sales and operations planning. As an example, consider how a premium paper supply chain uses aggregate planning to maximize profit. Many types of paper mills face seasonal demand that ripples up from cus- tomers to printers to distributors and finally to the manufacturers. Many types of premium paper have demand peaks in the spring, when annual reports are printed, and in the fall, when new-car brochures are released. Building a mill with capacity to meet demand in the spring and fall on an as-needed basis is too costly, because of the high cost of mill capacity. On the other side of the supply chain, premium papers often require special additives and coatings that may be in short supply. The paper manufacturer must deal with these constraints and maximize profit around them. To deal with these potential problems, mills use aggregate planning to determine production levels and inventory levels that they should build up in the slower months for sale in the spring and fall when demand is greater than the mill’s capacity. By taking into account the inputs from throughout the supply chain, aggregate planning allows the mill and the supply chain to maximize profit. The aggregate planner’s main objective is to identify the following operational parameters over the specified time horizon: Production Rate: the number of units to be completed per unit time (such as per week or per month) Workforce: the number of workers/units of capacity needed for production Overtime: the amount of overtime production planned Machine Capacity Level: the number of units of machine capacity needed for production Subcontracting: the subcontracted capacity required over the planning horizon Backlog: demand not satisfied in the period in which it arises but carried over to future periods Inventory on Hand: the planned inventory carried over the various periods in the planning horizon The aggregate plan serves as a broad blueprint for operations and establishes the parameters within which short-term production and distribution decisions are made. The aggregate plan allows the supply chain to alter capacity allocations and change supply contracts. As mentioned in earlier chapters, the entire supply chain should be involved with the planning process. If a manufacturer has planned an increase in production over a given time period, the supplier, transporter, and warehouser must be aware of this plan and incorporate the increase into their

Chapter 8 • Aggregate Planning in a Supply Chain 213 own plans. Ideally, all stages of the supply chain should work together on an aggregate plan that optimizes supply chain performance. If each stage develops its own aggregate plan independently, it is extremely unlikely that all the plans will mesh in a coordinated manner. This lack of coordination results in shortages or oversupply in the supply chain. Therefore, it is important to form aggregate plans over a wide scope of the supply chain. In the next section, we formally define the aggregate planning problem. We specify the information required for aggregate planning and discuss the decision outcomes that aggregate planning can provide. 8.2 THE AGGREGATE PLANNING PROBLEM The objective of the aggregate plan is to satisfy demand in a way that maximizes profit for the firm. We can state the aggregate planning problem formally as follows: Given the demand forecast for each period in the planning horizon, determine the production level, inventory level, capacity level (internal and outsourced), and any backlogs (unmet demand) for each period that maximize the firm’s profit over the planning horizon. To create an aggregate plan, a company must specify the planning horizon. A planning horizon is the time period over which the aggregate plan is to produce a solution—usually between 3 and 18 months. A company must also specify the duration of each period within the planning horizon (e.g., weeks, months, or quarters). In general, aggregate planning takes place over months or quarters. Next, a company specifies key information required to produce an aggregate plan and to make the decisions for which the aggregate plan will develop recommen- dations. This information and the recommendations are specified for a generic aggregate planning problem in this section. The model we propose in the next section is flexible enough to accommodate situation-specific requirements. An aggregate planner requires the following information: • Aggregate demand forecast Ft for each Period t in a planning horizon that extends over T periods • Production costs • Labor costs, regular time ($/hour), and overtime costs ($/hour) • Cost of subcontracting production ($/unit or $/hour) • Cost of changing capacity; specifically, cost of hiring/laying off workforce ($/worker) and cost of adding or reducing machine capacity ($/machine) • Labor/machine hours required per unit • Inventory holding cost ($/unit/period) • Stockout or backlog cost ($/unit/period) • Constraints • Limits on overtime • Limits on layoffs • Limits on capital available • Limits on stockouts and backlogs • Constraints from suppliers to the enterprise Using this information, a company makes the following determinations through aggregate planning: Production Quantity from Regular Time, Overtime, and Subcontracted Time: used to determine number of workers and supplier purchase levels Inventory Held: used to determine the warehouse space and working capital required

214 Chapter 8 • Aggregate Planning in a Supply Chain Backlog/Stockout Quantity: used to determine customer service levels Workforce Hired/Laid Off: used to determine any labor issues likely to be encountered Machine Capacity Increase/Decrease: used to determine if new production equipment should be purchased or available equipment idled The quality of an aggregate plan has a significant impact on the profitability of a firm. A poor aggregate plan can result in lost sales and lost profits if the available inventory and capacity are unable to meet demand. A poor aggregate plan may also result in a large amount of excess inventory and capacity, thereby raising costs. Therefore, aggregate planning is an important tool in helping a supply chain maximize profitability. Identifying Aggregate Units of Production An important first step in aggregate planning is the identification of a suitable aggregate unit of production. While planning is done at the aggregate level, it is important that the aggregate unit be identified in a way that when the final production schedule is built (this has to be at the disaggregate product level), the results of the aggregate plan reflect approximately what can be accomplished in practice. Given that the bottleneck is likely to be the most constraining area in any manufacturing facility, it is important to focus on the bottleneck when selecting the aggregate unit and identifying capacity as well as production times. When evaluating production times, it is also important to account for activities such as setups and maintenance that use up capacity but do not result in any production. Otherwise, the aggregate plan will overestimate the production capacity available, resulting in a plan that cannot be implemented in practice. We now discuss a simple approach that can be used to identify aggregate units and also evaluate costs, revenues, and times for this aggregate unit. Consider, for example, Red Tomato Tools, a manufacturer of gardening equipment with manufacturing facilities in Mexico. The company makes six product families at its manufactur- ing plant. The costs, revenues, production times, setup times, and historical batch sizes of production for each family are as shown in Table 8-1. In Table 8-1, the net production time per unit is obtained by adding the changeover time allocated to each unit and the production time. Thus, the net production time/unit for Family A is obtained as 8/50 + 5.60 = 5.76 hours. A simple approach to defining the aggregate unit is based on the weighted average of the percentage of sales represented by each family. Such an approach is meaningful if management is relatively confident of the mix of sales and all the product families use roughly the same set of resources at a plant. Taking this approach, the material cost per aggregate unit is obtained as (15 * 0.10) + (7 * 0.25) + (9 * 0.20) + (12 * 0.10) + (9 * 0.20) + (13 * 0.15) = $10. Using a similar evaluation, we obtain that the revenue per aggregate unit = $40 and the net production time per aggregate unit = 4.00 hours. Table 8-1 Costs, Revenues, and Times at Red Tomato Tools Family Material Revenue/ Setup Average Production Net Percentage Cost/ Unit ($) Time/Batch Batch Size Time/ Production Share of A Time/Unit Units Sold B Unit ($) 54 (hour) 50 Unit (hour) C 30 150 (hour) 10 D 15 39 8 100 5.60 25 E 7 49 6 3.00 5.76 20 F 9 36 8 50 3.80 3.04 10 48 10 100 4.80 3.88 20 12 6 3.60 5.00 15 9 5 75 4.30 3.66 4.37 13

Chapter 8 • Aggregate Planning in a Supply Chain 215 Other potential aggregate units could be tons of output (likely to be suitable for continuous flows such as gasoline or paper) or dollars of sales. For example, a paper mill might produce papers of different thickness and quality. If tons of output is used as the aggregate unit, all capacity, cost, and revenue calculations should account for the product mix. 8.3 AGGREGATE PLANNING STRATEGIES The aggregate planner must make trade-offs among capacity, inventory, and backlog costs. An aggregate plan that increases one of these costs typically results in reduction of the other two. In this sense, the costs represent a trade-off: To lower inventory cost, a planner must increase capacity cost or delay delivery to the customer. Thus, the planner trades inventory cost for capacity or backlog cost. Arriving at the most profitable combination of trade-offs is the goal of aggregate planning. Given that demand varies over time, the relative level of the three costs leads to one of them being the key lever the planner uses to maximize profits. If the cost of varying capacity is low, a company may not need to build inventory or carry backlogs. If the cost of varying capacity is high, a company may compensate by building some inventory and carrying some backlogs from peak demand periods to off-peak demand periods. In general, a company attempts to use a combination of the three costs to best meet demand. Therefore, the fundamental trade-offs available to a planner are among • Capacity (regular time, overtime, subcontracted) • Inventory • Backlog/lost sales because of delay There are essentially three distinct aggregate planning strategies for achieving balance among these costs. These strategies involve trade-offs among capital investment, workforce size, work hours, inventory, and backlogs/lost sales. Most strategies that a planner actually uses are a combination of these three and are referred to as tailored or hybrid strategies. The three strate- gies are as follows: 1. Chase strategy—using capacity as the lever: With this strategy, the production rate is synchronized with the demand rate by varying machine capacity or hiring and laying off employees as the demand rate varies. In practice, achieving this synchronization can be problem- atic because of the difficulty of varying capacity and workforce on short notice. This strategy can be expensive to implement if the cost of varying machine or labor capacity over time is high. It can also have a significant negative impact on the morale of the workforce. The chase strategy results in low levels of inventory in the supply chain and high levels of change in capacity and workforce. It should be used when the cost of carrying inventory is high and costs to change levels of machine and labor capacity are low. 2. Flexibility strategy—using utilization as the lever: This strategy may be used if there is excess machine capacity (i.e., if machines are not used 24 hours a day, seven days a week) and the workforce shows scheduling flexibility. In this case, the workforce (capacity) is kept stable, but the number of hours worked is varied over time in an effort to synchronize production with demand. A planner can use variable amounts of overtime or a flexible schedule to achieve this synchronization. Although this strategy does require that the workforce be flexible, it avoids some of the problems associated with the chase strategy, most notably, changing the size of the workforce. This strategy results in low levels of inventory but with lower average machine utilization. It should be used when inventory carrying costs are relatively high and machine capacity is relatively inexpensive. 3. Level strategy—using inventory as the lever: With this strategy, a stable machine capacity and workforce are maintained with a constant output rate. Shortages and surpluses result in inventory levels fluctuating over time. In this case, production is not synchronized with demand. Either inventories are built up in anticipation of future demand or backlogs are carried

216 Chapter 8 • Aggregate Planning in a Supply Chain over from high- to low-demand periods. Employees benefit from stable working conditions. A drawback associated with this strategy is that large inventories may accumulate and customer orders may be delayed. This strategy keeps capacity and costs of changing capacity relatively low. It should be used when inventory carrying and backlog costs are relatively low. In practice, a planner is most likely to come up with a tailored or hybrid strategy that combines aspects of all three approaches. In the next section, we discuss a methodology that is commonly used for aggregate planning. 8.4 AGGREGATE PLANNING USING LINEAR PROGRAMMING As we discussed earlier, the goal of aggregate planning is to maximize profit while meeting demand. Every company, in its effort to meet customer demand, faces certain constraints, such as the capacity of its facilities or a supplier’s ability to deliver a component. A highly effective tool for a company to use when it tries to maximize profits while being subjected to a series of constraints is linear programming. Linear programming finds the solution that creates the highest profit while satisfying the constraints that the company faces. We illustrate linear programming through the discussion of Red Tomato Tools, a small manufacturer of gardening equipment with manufacturing facilities in Mexico. Red Tomato’s products are sold through retailers in the United States. Red Tomato’s operations consist of the assembly of purchased parts into a multipurpose gardening tool. Because of the limited equipment and space required for its assembly operations, Red Tomato’s capacity is determined mainly by the size of its workforce. For this example, we use a six-month time period because this is a long enough time horizon to illustrate many of the main points of aggregate planning. Red Tomato Tools The demand for Red Tomato’s gardening tools from consumers is highly seasonal, peaking in the spring as people plant their gardens. This seasonal demand ripples up the supply chain from the retailer to Red Tomato, the manufacturer. The options Red Tomato has for handling the season- ality are adding workers during the peak season, subcontracting out some of the work, building up inventory during the slow months, or building up a backlog of orders that will be delivered late to customers. To determine how to best use these options through an aggregate plan, Red Tomato’s vice president of supply chain starts with the first task—building a demand forecast. Although Red Tomato could attempt to forecast this demand itself, a much more accurate fore- cast comes from a collaborative process used by both Red Tomato and its retailers to produce the forecast shown in Table 8-2. It is important that this demand account for the product mix that is expected to sell and be in terms of aggregate units defined earlier. Red Tomato sells each tool through retailers for $40. The company has a starting inventory in January of 1,000 tools. At the beginning of January, the company has a workforce of 80 employees. Table 8-2 Demand Forecast at Red Tomato Tools Month Demand Forecast January 1,600 February 3,000 March 3,200 April 3,800 May 2,200 June 2,200

Chapter 8 • Aggregate Planning in a Supply Chain 217 Table 8-3 Costs for Red Tomato Item Cost Material cost $10/unit Inventory holding cost $2/unit/month Marginal cost of stockout/backlog $5/unit/month Hiring and training costs $300/worker Layoff cost $500/worker Labor hours required 4/unit Regular time cost $4/hour Overtime cost $6/hour Cost of subcontracting $30/unit The plant has a total of 20 working days in each month, and each employee earns $4 per hour regular time. Each employee works eight hours per day on straight time and the rest on overtime. As discussed previously, the capacity of the production operation is determined primarily by the total labor hours worked. Therefore, machine capacity does not limit the capacity of the production operation. Because of labor rules, no employee works more than 10 hours of overtime per month. The various costs are shown in Table 8-3. It is important that the costs and labor hours be in aggregate units as discussed in Section 8.2. Currently, Red Tomato has no limits on subcontracting, inventories, and stockouts/ backlog. All stockouts are backlogged and supplied from the following months’ production. Inventory costs are incurred on the ending inventory in the month. The supply chain manager’s goal is to obtain the optimal aggregate plan that allows Red Tomato to end June with at least 500 units (i.e., no stockouts at the end of June and at least 500 units in inventory). The optimal aggregate plan is one that results in the highest profit over the six-month planning horizon. For now, given Red Tomato’s desire for a high level of customer service, assume all demand is to be met, although it can be met late. Therefore, the revenues earned over the planning horizon are fixed. As a result, minimizing cost over the planning horizon is the same as maximizing profit. In many instances, a company has the option of not meeting certain demand, or price itself may be a variable that a company has to determine based on the aggregate plan. In such a scenario, minimizing cost is not equivalent to maximizing profits. Decision Variables The first step in constructing an aggregate planning model is to identify the set of decision variables whose values are to be determined as part of the aggregate plan. For Red Tomato, the following decision variables are defined for the aggregate planning model: Wt = workforce size for Month t, t = 1, . . . , 6 Ht = number of employees hired at the beginning of Month t, t = 1, . . . , 6 Lt = number of employees laid off at the beginning of Month t, t = 1, . . . , 6 Pt = number of units produced in Month t, t = 1, . . . , 6 It = inventory at the end of Month t, t = 1, . . . , 6 St = number of units stocked out/backlogged at the end of Month t, t = 1, . . . , 6 Ct = number of units subcontracted for Month t, t = 1, . . . , 6 Ot = number of overtime hours worked in Month t, t = 1, . . . , 6 The next step in constructing an aggregate planning model is to define the objective function.

218 Chapter 8 • Aggregate Planning in a Supply Chain Objective Function Denote the demand in Period t by Dt. The values of Dt are as specified by the demand forecast in Table 8-2. The objective function is to minimize the total cost (equivalent to maximizing total profit as all demand is to be satisfied) incurred during the planning horizon. The cost incurred has the following components: • Regular-time labor cost • Overtime labor cost • Cost of hiring and layoffs • Cost of holding inventory • Cost of stocking out • Cost of subcontracting • Material cost These costs are evaluated as follows: 1. Regular-time labor cost. Recall that workers are paid a regular-time wage of $640 ($4/hour * 8 hours/day * 20 days/month) per month. Because Wt is the number of workers in Period t, the regular-time labor cost over the planning horizon is given by 6 Regular-time labor cost = a 640Wt t=1 2. Overtime labor cost. As overtime labor cost is $6 per hour (see Table 8-3) and Ot rep- resents the number of overtime hours worked in Period t, the overtime cost over the planning horizon is 6 Overtime labor cost = a 6Ot t=1 3. Cost of hiring and layoffs. The cost of hiring a worker is $300 and the cost of laying off a worker is $500 (see Table 8-3). Ht and Lt represent the number hired and the number laid off, respectively, in Period t. Thus, the cost of hiring and layoff is given by 66 Cost of hiring and layoff = a 300Ht + a 500Lt t=1 t=1 4. Cost of inventory and stockout. The cost of carrying inventory is $2 per unit per month, and the cost of stocking out is $5 per unit per month (see Table 8-3). It and St represent the units in inventory and the units stocked out, respectively, in Period t. Thus, the cost of hold- ing inventory and stocking out is 66 Cost of holding inventory and stocking out = a 2It + a 5St t=1 t=1 5. Cost of materials and subcontracting. The material cost is $10 per unit and the subcontracting cost is $30/unit (see Table 8-3). Pt represents the quantity produced and Ct represents the quantity subcontracted in Period t. Thus, the material and subcontracting cost is 66 Cost of materials and subcontracting = a 10Pt + a 30Ct t=1 t=1

Chapter 8 • Aggregate Planning in a Supply Chain 219 The total cost incurred during the planning horizon is the sum of all the aforementioned costs and is given by 6 66 6 6 (8.1) a 640Wt + a 6Ot + a 300Ht + a 500Lt + a 2It t=1 t=1 t=1 t=1 t=1 66 6 + a 5St + a 10Pt + a 30Ct t=1 t=1 t=1 Red Tomato’s objective is to find an aggregate plan that minimizes the total cost (Equation 8.1) incurred during the planning horizon. The values of the decision variables in the objective function cannot be set arbitrarily. They are subject to a variety of constraints defined by available capacity and operating policies. The next step in setting up the aggregate planning model is to define clearly the constraints linking the decision variables. Constraints Red Tomato’s vice president must now specify the constraints that the decision variables must not violate. They are as follows: 1. Workforce, hiring, and layoff constraints. The workforce size Wt in Period t is obtained by adding the number hired Ht in Period t to the workforce size Wt-1 in Period t - 1, and subtracting the number laid off Lt in Period t as follows: Wt = Wt-1 + Ht - Lt for t = 1, Á , 6 (8.2) The starting workforce size is given by W0 = 80. 2. Capacity constraints. In each period, the amount produced cannot exceed the available capacity. This set of constraints limits the total production by the total internally available capacity (which is determined based on the available labor hours, regular or overtime). Subcontracted production is not included in this constraint because the constraint is limited to production within the plant. As each worker can produce 40 units per month on regular time (four hours per unit as specified in Table 8-3) and one unit for every four hours of overtime, we have the following: Pt … 40Wt + Ot for t = 1, Á , 6 (8.3) 4 3. Inventory balance constraints. The third set of constraints balances inventory at the end of each period. Net demand for Period t is obtained as the sum of the current demand Dt and the previous backlog St-1. This demand is either filled from current production (in-house production Pt or subcontracted production Ct) and previous inventory It-1 (in which case some inventory It may be left over) or part of it is backlogged St. This relationship is captured by the following equation: It-1 + Pt + Ct = Dt + St-1 + It - St for t = 1, Á , 6 (8.4) The starting inventory is given by I0 = 1,000, the ending inventory must be at least 500 units (i.e., I6 Ú 500), and initially there are no backlogs (i.e., S0 = 0). 4. Overtime limit constraints. The fourth set of constraints requires that no employee work more than 10 hours of overtime each month. This requirement limits the total amount of overtime hours available as follows: Ot … 10Wt for t = 1, Á , 6 (8.5)

220 Chapter 8 • Aggregate Planning in a Supply Chain In addition, each variable must be nonnegative and there must be no backlog at the end of Period 6 (i.e., S6 = 0). When implementing the model in Microsoft Excel, which we discuss later, it is easiest if all the constraints are written so that the right-hand side for each constraint is 0. The overtime limit constraint (Equation 8.5) in this form is written as Ot - 10Wt … 0 for t = 1, Á , 6 Observe that one can easily add constraints that limit the amount purchased from subcontrac- tors each month or the maximum number of employees to be hired or laid off. Any other constraints limiting backlogs or inventories can also be accommodated. Ideally, the number of employees hired or laid off should be integer variables. Fractional variables may be justified if some employees work for only part of a month. Such a linear program can be solved using the tool Solver in Excel. If we assume the average inventory in Period t to be the average of the starting and ending inventories, that is, 1It-1 + It2>2, the average inventory over the planning horizon is given by 1I0 + IT2>2 + a a tT=-11It b Average inventory = T The average time that units spend in inventory over the planning horizon is obtained using Little’s law (average flow time = average inventory/throughput). The average time in inventory is given as (I0 + IT)>2 + a a Tt =-11It b Æ a a tT=-11Dt b J T KJ T K Average time in inventory = (8.6) By optimizing the objective function (minimizing cost in Equation 8.1) subject to the listed constraints (Equations 8.2 to 8.5), the vice president obtains the aggregate plan shown in Table 8-4. (Later in the chapter, we discuss how to perform this optimization using Excel.) For this aggregate plan we have the following: Total cost over planning horizon = $422,660 Red Tomato lays off a total of 16 employees at the beginning of January. After that, the company maintains the workforce and production level. They use the subcontractor during Table 8-4 Aggregate Plan for Red Tomato Period, No. Hired, No. Workforce Overtime, Inventory, Stockout, Subcontract, Total t Ht Laid Size, Ot It St Ct Production, Off, Lt Wt 0 0 0 1,000 0 0 Pt 1 0 0 80 0 1,960 0 0 2 0 16 64 0 1,520 0 0 2,560 3 0 64 0 0 0 2,560 4 0 0 64 0 880 220 140 2,560 5 0 0 64 0 0 0 0 2,560 6 0 0 64 0 0 0 2,560 0 64 140 2,560 0 500

Chapter 8 • Aggregate Planning in a Supply Chain 221 the month of April. They carry a backlog only from April to May. In all other months, they plan no stockouts. In fact, Red Tomato carries inventory in all other periods. We describe this inventory as seasonal inventory because it is carried in anticipation of a future increase in demand. Given the sale price of $40 per unit and total sales of 16,000 units, revenue over the planning horizon is given by Revenue over planning horizon = 40 * 16,000 = $640,000 The average seasonal inventory during the planning horizon is given by (I0 + I6) n 2 + aa 5 1Itb 5,250 t= Average seasonal inventory = = = 875 T6 The average flow time for this aggregate plan over the planning horizon (using Equation 8.6) is given by Average flow time = 875 = 0.33 = 0.33 months 2,667 If the seasonal fluctuation of demand grows, synchronization of supply and demand becomes more difficult, resulting in an increase in either inventory or backlogs as well as an increase in the total cost to the supply chain. This is illustrated in Example 8-1, in which the demand forecast is more variable. EXAMPLE 8-1 Impact of Higher Demand Variability All the data are exactly the same as in our previous discussion of Red Tomato, except for the demand forecast. Assume that the same overall demand (16,000 units) is distributed over the six months in such a way that the seasonal fluctuation of demand is higher, as shown in Table 8-5. Obtain the optimal aggregate plan in this case. Analysis: In this case, the optimal aggregate plan (using the same costs as those used before) is shown in Table 8-6. Observe that monthly production remains the same, but both inventories and stockouts (backlogs) go up compared to the aggregate plan in Table 8-4 for the demand profile in Table 8-2. The cost of meeting the new demand profile in Table 8-5 is higher at $433,080 (compared to $422,660 for the previous demand profile in Table 8-2). Table 8-5 Demand Forecast with Higher Seasonal Fluctuation Month Demand Forecast January 1,000 February 3,000 March 3,800 April 4,800 May 2,000 June 1,400

222 Chapter 8 • Aggregate Planning in a Supply Chain Table 8-6 Optimal Aggregate Plan for Demand in Table 8-5 Period, No. Hired, No. Laid Workforce Overtime, Inventory, Stockout, Subcontract, Total Production, t Ht Off, Lt Size, Wt Ot It St Ct Pt 0 0 0 80 0 1,000 0 0 1 0 16 64 0 2,560 0 0 2,560 2,560 2 0 0 64 0 2,120 0 0 2,560 2,560 3 0 0 64 0 880 0 140 2,560 2,560 4 0 0 64 0 0 1,220 0 5 0 0 64 0 0 660 0 6 0 0 64 0 500 0 0 The seasonal inventory during the planning horizon is given by Seasonal inventory = [(I0 + IT)>2] + a tT=-11It = 6,310 = 1,052 T6 The average flow time for this aggregate plan over the planning horizon (using Equation 8.6) is given by Average flow time = 1,052 = 0.39 months 2,667 From Example 8-1, we can see that the increase in demand variability at the retailer increases seasonal inventory as well as planned costs. Using the Red Tomato example, we also see that the optimal trade-off changes as the costs change. This is illustrated in Example 8-2, in which we show that as the costs of hiring and layoff decrease, it is better to vary capacity with demand while having less inventory and backlogs. EXAMPLE 8-2 Impact of Lower Costs of Hiring and Layoff Assume that demand at Red Tomato is as shown in Table 8-2, and all other data are the same except that the costs of hiring and layoff are now $50 each. Evaluate the total cost corresponding to the aggregate plan in Table 8-4. Suggest an optimal aggregate plan for the new cost structure. Analysis: If the costs of hiring and layoff decrease to $50 each, the cost corresponding to the aggregate plan in Table 8-4 decreases from $422,660 to $412,780. Taking this new cost into account and determining a new optimal aggregate plan yields the plan shown in Table 8-7. Observe that the workforce size fluctuates between a high of 87 and a low of 45, as opposed to being stable at 64 as in Table 8-4. As expected, the workforce size is varied (because the cost of varying capacity has decreased) while inventory and stockouts have decreased compared to the aggregate plan in Table 8-4. The total cost of the aggregate plan in Table 8-7 is $412,780, compared to $422,660 (for the aggregate plan in Table 8-4) if the cost of hiring and layoff is $50 each.

Chapter 8 • Aggregate Planning in a Supply Chain 223 Table 8-7 Optimal Aggregate Plan for Hiring and Layoff Cost of $50/Worker Period, No. Hired, No. Laid Off, Workforce Overtime, Inventory, Stockout, Subcontract, Total Production, t Ht Ot Size, Wt Ot It St Ct Pt 00 0 80 0 1,000 0 0 0 10 35 45 0 1,200 0 1,800 1,800 20 0 45 0 00 0 3,480 3,480 3 42 0 87 0 280 0 0 2,440 2,480 40 0 87 0 0 20 20 5 0 26 61 0 220 0 0 61 0 62 0 500 0 0 The seasonal inventory during the planning horizon is given by Seasonal inventory = [(I0 + IT)>2] + a Tt=-11It = 2,450 = 408 T6 The average flow time for this aggregate plan over the planning horizon (using Equation 8.6) is given by Average flow time = 408 = 0.15 months 2,667 From Example 8-2, observe that increasing volume flexibility (by decreasing the cost of hiring and layoff) not only decreases the total cost but also shifts the optimal balance toward using the volume flexibility while carrying lower inventories and allowing less stockout. Forecast Error in Aggregate Plans The aggregate planning methodology we have discussed in this chapter does not take into account any forecast error. However, we know that all forecasts have errors. To improve the quality of these aggregate plans, forecast errors must be considered. Forecasting errors are dealt with using either safety inventory, defined as inventory held to satisfy demand that is higher than forecasted (discussed thoroughly in Chapter 12), or safety capacity, defined as capacity used to satisfy demand that is higher than forecasted. A company can create a buffer for forecast error using safety inventory and safety capacity in a variety of ways, some of which are listed next: • Use overtime as a form of safety capacity. • Carry extra workforce permanently as a form of safety capacity. • Use subcontractors as a form of safety capacity. • Build and carry extra inventories as a form of safety inventory. • Purchase capacity or product from an open or spot market as a form of safety capacity. In the next section, we explain how to implement the linear programming methodology for aggregate planning using Microsoft Excel.

224 Chapter 8 • Aggregate Planning in a Supply Chain 8.5 AGGREGATE PLANNING IN EXCEL Next we discuss how to generate the aggregate plan for Red Tomato in Table 8-4 using Excel. To access Excel’s linear programming capabilities, use Solver (Data | Analysis | Solver). To begin, we need to create a table, which we illustrate with Figure 8-1, containing the following decision variables: Wt = workforce size for Month t, t = 1, . . . , 6 Ht = number of employees hired at the beginning of Month t, t = 1, . . . , 6 Lt = number of employees laid off at the beginning of Month t, t = 1, . . . , 6 Pt = number of units produced in Month t, t = 1, . . . , 6 It = inventory at the end of Month t, t = 1, . . . , 6 St = number of units stocked out at the end of Month t, t = 1, . . . , 6 Ct = number of units subcontracted for Month t, t = 1, . . . , 6 Ot = number of overtime hours worked in Month t, t = 1, . . . , 6 Figure 8-1 illustrates what this table should look like. The decision variables are contained in cells B5 to I10, with each cell corresponding to a decision variable. For example, cell D7 corre- sponds to the workforce size in Period 3. Begin by setting all the decision variables to 0 as shown in Figure 8-1. Also note that column J contains the actual demand. The demand information is included because it is required to calculate the aggregate plan. The second step is to construct a table for the constraints in Equations 8.2 to 8.5. The constraint table may be constructed as shown in Figure 8-2. Column M contains workforce constraints (Equation 8.2), column N contains capacity constraints (Equation 8.3), column O contains inventory balance constraints (Equation 8.4), and column P contains overtime constraints (Equation 8.5). These constraints are applied to each of the six periods. Each constraint will eventually be written in Solver as Cell value {…, =, or Ú} 0 In our case, we have constraints M5:M10 = 0, N5:N10 Ú 0, O5:O10 = 0, P5:P10 Ú 0 The third step is to create a cell containing the objective function, which is how each solution is judged. This cell need not contain the entire formula but can be written as a FIGURE 8-1 Spreadsheet Area for Decision Variables

Chapter 8 • Aggregate Planning in a Supply Chain 225 Cell Cell Formula Equation Copied to M6:M10 M5 =D5 - D4 - B5 + C5 8.2 N6:N10 O6:O10 N5 =40*D5 + E5/4 -I5 8.3 P6:P10 O5 =F4-G4+I5+H5-J5-F5+G5 8.4 P5 =-E5 + 10*D5 8.5 FIGURE 8-2 Spreadsheet Area for Constraints formula using cells with intermediate cost calculations. For the Red Tomato example, the spreadsheet area for cost calculations is shown in Figure 8-3. Cell B15, for instance, contains the hiring costs incurred in Period 1. The formula in cell B15 is the product of cell B5 and the cell containing the hiring cost per worker, which is obtained from Table 8-3. Other cells are filled similarly. Cell C22 contains the sum of cells B15 to I20, representing the total cost. The fourth step is to use Data | Analysis | Solver to invoke Solver. Within the Solver Parameters dialog box, enter the following information to represent the linear programming model: Set Target Cell: C22 Equal to: Select Min By Changing Cells: B5:I10 Subject to the constraints: B5:C10 ϭ integer {Number of workers hired or laid off is integer} B5:I10 Ú 0 {All decision variables are nonnegative} F10 Ú 500 {Inventory at end of Period 6 is at least 500} G10 = 0 {Stockout at end of Period 6 equals 0} FIGURE 8-3 Spreadsheet Area for Cost Calculations

226 Chapter 8 • Aggregate Planning in a Supply Chain FIGURE 8-4 Solver Parameters Dialog Box M5:M10 = 0 {Wt - Wt-1 - Ht + Lt = 0 for t = 1, Á , 6} N5:N10 Ú 0 {40Wt + Ot>4 - Pt Ú 0 for t = 1, Á , 6} O5:O10 = 0 {It-1 - St-1 + Pt + Ct - Dt - It + St = 0 for t = 1, Á , 6} P5:P10 Ú 0 {10Wt - Ot Ú 0 for t = 1, Á , 6} The Solver Parameters dialog box is shown in Figure 8-4. Click on Solve. The optimal solution should be returned. If Solver does not return the optimal solution, solve the problem again after saving the solution that Solver has returned. (In some cases, multiple repetitions of this step may be required because of some flaws in the version of Solver that comes with Excel. Add-ins are available at relatively low cost that do not have any of these issues.) The optimal solution turns out to be the one shown in Table 8-4. 8.6 BUILDING A ROUGH MASTER PRODUCTION SCHEDULE From an aggregate plan, a planner must disaggregate the available information and build a rough master production schedule (MPS) that identifies the batches produced in each period at the level of each product family. We return to the Red Tomato example to illustrate a simple approach to disaggregate an aggregate plan. While this approach is not necessarily optimal, it is simple to implement and allows for a feasibility check. More sophisticated methods (e.g., see Bitran and Hax (1981)) are available if a planner wants to search for better solutions. These methods, however, are difficult to implement and may not be able to reflect all the complex realities. It is for this reason that we propose this simple approach. Consider the aggregate plan in Table 8-4. The plan calls for a workforce of 64 and a production of 2,560 aggregate units in Period 1. We know that the production constraint is feasible at the aggregate level, but we will need to check feasibility at the disaggregate level. The first step is to divide the production quantity of 2,560 across the six families. We do so in the ratio of expected sales as shown in Table 8-8. Thus, the plan is to produce 256 units of Family A in Period 1 because it represents 10 percent of sales. The next step is to identify the number of planned batches for each family. To get feasibility of the plan, we divide the planned production quantity by the average batch size and the round the answer down. For Family A, the planned number of setups (batches) is thus 256/50 = 5.12 rounded down, which equals 5. As a result, the average batch size of Family A produced in this period will be larger than 50 (about 51). We similarly obtain the planned number of setups (batches) for each of the other families in Period 1 as shown in Table 8-8. To check the feasibility of the planned schedule, we calculate the setup time and the production time for the planned number of

Chapter 8 • Aggregate Planning in a Supply Chain 227 Table 8-8 Disaggregating the Aggregate Plan at Red Tomato Tools for Period 1 Family Setup Average Production Production Number of Setup Time Production Time Time/Batch Batch Size Time/Unit Quantity Setups (hours) (hours) (hour) (hour) 1,433.6 1,920.0 A8 50 5.60 256 5 40 1,945.6 B6 150 3.00 640 4 24 1,228.8 C8 100 3.80 512 5 40 1,843.2 D 10 5 50 1,651.2 E6 50 4.80 256 5 30 F5 100 3.60 512 5 25 75 4.30 384 batches and units of each product family. From Table 8-8, the total planned production and setup time is 10,231.4 hours (209 for setup + 10,022.4 for production). Given the 64 people planned, the available production time in the period is 64 * 160 = 10,240 hours. The planned schedule thus seems feasible. 8.7 THE ROLE OF IT IN AGGREGATE PLANNING Aggregate planning is arguably the supply chain area in which information technology has been used the most. The earliest IT supply chain products were aggregate planning modules, often called factory, production, or manufacturing planning. Some of the early modules focused only on obtaining a feasible production plan subject to constraints arising from demand and available capacity. Later modules provided tools that chose an optimal solution from among the feasible production plans, based on objectives such as increased output or lowered cost. These classic solutions generally formulated the aggregate planning problem as a linear program (LP) to get a production schedule of products to be made in each period of time. Today, some planning modules incorporate nonlinear optimization to account for the fact that not all constraints or reasonable objective functions are linear functions. However, given the large amount of data considered in producing aggregate plans, which can render nonlinear problems computationally prohibitive, and the ability to create linear approxi- mations of nonlinear functions, linear programming is often the best way to solve these problems. Supply chain planning modules today often combine both production planning and inventory planning. The supply chain planning module uses the output of the forecasting module as a constraint in setting up the production schedule and inventory levels. These production schedules and inventory levels are used by the execution system for the actual pro- duction of the goods and the setting of inventory levels throughout the supply chain. Given the complexity of the problem, aggregate planning modules can add significant value even for small companies. IT can add value in the aggregate planning realm along a number of dimensions: • The ability to handle large problems • The ability to handle complex problems (through either nonlinear optimization or linear approximations) • The ability to interact with other core IT systems such as inventory management and sourcing Because aggregate planning problems are so complex, there is often no other way to arrive at a feasible solution than through IT.

228 Chapter 8 • Aggregate Planning in a Supply Chain Major software players in this area include the ERP software firms (SAP and Oracle) and a variety of other vendors who often specialize their planning software by industry verticals. In the last decade, SAP and Oracle have come to dominate this space with specialized vendors find- ing it harder to survive. 8.8 IMPLEMENTING AGGREGATE PLANNING IN PRACTICE 1. Think beyond the enterprise to the entire supply chain. Most aggregate planning today takes only the enterprise as its breadth of scope. However, many factors outside the enter- prise and throughout the supply chain can affect the optimal aggregate plan dramatically. Therefore, avoid the trap of thinking only about your enterprise when planning. Work with downstream partners to produce forecasts, with upstream partners to determine constraints, and with any other supply chain entities that can improve the quality of the inputs into the aggregate plan. The plan is only as good as the quality of the inputs. So using the supply chain to increase the quality of the inputs will greatly improve the quality of the aggregate plan. Also make sure to communicate the aggregate plan to all supply chain partners who will be affected by it. 2. Make plans flexible, because forecasts are always inaccurate. Aggregate plans are based on forecasts of future demand. Given that these forecasts are always inaccurate to some degree, the aggregate plan needs to have some flexibility built into it if it is to be useful. By building flexibility into the plan, when future demand changes, or other changes occur such as increases in costs, the plan can adjust appropriately to handle the new situation. How do we create this flexibility? In addition to the suggestions earlier in the chapter, we recommend that a manager perform sensitivity analysis on the inputs into an aggregate plan. For example, if the plan recommends expanding expensive capacity while facing uncertain demand, examine the outcome of a new aggregate plan when demand is higher and lower than expected. If this examination reveals a small savings from expanding capacity when demand is high but a large increase in cost when demand is lower than expected, deciding to postpone the capacity investment decision is a potentially attractive option. Using sensitivity analysis on the inputs into the aggregate plan enables a planner to choose the best solution for the range of possibilities that could occur. 3. Rerun the aggregate plan as new data emerge. As we have mentioned, aggregate plans provide a map for the next 3 to 18 months. This does not mean that a firm should run aggregate plans only once every 3 to 18 months. As inputs such as demand forecasts change, managers should use the latest values of these inputs and rerun the aggregate plan. By using the latest inputs, the plan will avoid suboptimization based on old data and will produce a better solution. 4. Use aggregate planning as capacity utilization increases. Surprisingly, many compa- nies do not create aggregate plans and instead rely solely on orders from their distributors or warehouses to determine their production schedules. These orders are driven either by actual demand or through inventory management algorithms. If a company has no trouble meeting demand efficiently this way, then the lack of aggregate planning may not harm the company signif- icantly. However, when utilization becomes high and capacity is an issue, relying on orders to set the production schedule can lead to capacity problems. When utilization is high, the likelihood of producing for all the orders as they arrive is low. Planning needs to be done to best utilize the capacity to meet the forecasted demand. Therefore, as capacity utilization increases, it becomes more important to perform aggregate planning. 8.9 SUMMARY OF LEARNING OBJECTIVES 1. Identify the decisions that are best solved by aggregate planning. Aggregate planning is best used to determine capacity, production, and inventory decisions for each period of time over a range of 3 to 18 months. It is most important to perform aggregate planning when capacity is limited and lead times are long.

Chapter 8 • Aggregate Planning in a Supply Chain 229 2. Understand the importance of aggregate planning as a supply chain activity. Aggregate planning has a significant impact on supply chain performance and must be viewed as an activity that involves all supply chain partners. An aggregate plan prepared by an enterprise in isolation is not very useful because it does not take into account all requirements of the customer stage and constraints from the supplier stage. Localized aggregate planning cannot do a good job of matching supply and demand. Good aggregate planning is done in collaboration with both customers and suppliers because accurate input is required from both stages. The quality of these inputs, in terms of both the demand forecast to be met and the constraints to be dealt with, determines the quality of the aggregate plan. The results of the aggregate plan must also be shared across the supply chain because they influence activities for both customers and suppliers. For suppliers, the aggregate plan determines anticipated orders; for customers, the aggregate plan determines planned supply. 3. Describe the information needed to produce an aggregate plan. To create an aggre- gate plan, a planner needs a demand forecast, cost and production information, and any supply constraints. The demand forecast consists of an estimate of demand for each period of time in the planning horizon. The production and cost data consist of capacity levels and costs to raise and lower them, production costs, costs to store the product, costs of stocking out the product, and any restrictions that limit these factors. Supply constraints determine limits on outsourcing, overtime, or materials. 4. Explain the basic trade-offs to consider when creating an aggregate plan. The basic trade-offs involve balancing the cost of capacity, the cost of inventory, and the cost of stockouts to maximize profitability. Increasing any one of the three allows the planner to lower the other two. 5. Formulate and solve aggregate planning problems using Microsoft Excel. Aggregate planning problems can be solved in Excel by setting up cells for the objective function and the constraints and using the Solver to produce the solution. Discussion Questions 6. How does the availability of subcontracting affect the aggre- gate planning problem? 1. What are some industries in which aggregate planning would be particularly important? 7. If a company currently employs the chase strategy and the cost of training increases dramatically, how might this change 2. What are the characteristics of the industries from Question 1 the company’s aggregate planning strategy? that make them good candidates for aggregate planning? 8. What are some key issues to consider when picking an aggre- 3. What are the main differences among the aggregate planning gate unit of analysis? strategies? 9. How can aggregate planning be used in an environment of 4. What types of industries or situations are best suited to the high demand uncertainty? chase strategy? The flexibility strategy? The level strategy? 5. What are the major cost categories needed as inputs for aggre- gate planning? Exercises phone total 20 euros. Given the rapid decline in component and finished-product prices, carrying inventory from one 1. Skycell, a major European cell phone manufacturer, is making month to the next incurs a cost of 3 euros per phone per production plans for the coming year. Skycell has worked month. Skycell currently has a no-layoff policy in place. with its customers (the service providers) to come up with Overtime is limited to a maximum of 20 hours per month forecasts of monthly requirements (in thousands of phones) as per employee. Assume that Skycell has a starting inventory shown in Table 8-9. of 50,000 units and wants to end the year with the same Manufacturing is primarily an assembly operation, level of inventory. and capacity is governed by the number of people on the production line. The plant operates for 20 days a month, a. Assuming no backlogs, no subcontracting, and no new eight hours each day. One person can assemble a phone hires, what is the optimum production schedule? What is every 10 minutes. Workers are paid 20 euros per hour and the annual cost of this schedule? a 50 percent premium for overtime. The plant currently employs 1,250 workers. Component costs for each cell

230 Chapter 8 • Aggregate Planning in a Supply Chain Table 8-9 Monthly Demand for Cell Phones, 50 people who are willing to work as seasonal employees. in Thousands The cost of bringing them on is 800 euros per employee, and the layoff cost is 1,200 euros per employee. Month Demand a. What is the optimal production, hiring, and layoff schedule? January 1,000 b. How does the optimal schedule change if the seasonal February 1,100 March 1,000 pool grows from 50 to 100? April 1,200 c. Relative to having 1,250 permanent employees and May 1,500 June 1,600 50 seasonal, will Skycell gain significantly if it carries July 1,600 only 1,100 permanent employees but has 200 seasonal August employees? September 900 d. Consider the case in which Skycell has 1,250 permanent October 1,100 employees and 50 seasonal employees. Does Skycell November gain more by eliminating its no-layoff policy for its December 800 permanent employees or by increasing the seasonal 1,400 employee pool from 50 to 100? Assume permanent 1,700 employees can be hired or laid off at the same cost as the seasonal employees. b. Is there any value for management to negotiate an increase of allowed overtime per employee per month 4. FlexMan, an electronics contract manufacturer, uses its from 20 hours to 40? Topeka, Kansas, facility to produce two product categories: routers and switches. Consultation with customers has indi- c. Reconsider parts (a) and (b) if Skycell starts with only cated a demand forecast for each category over the next 12 1,200 employees. Reconsider parts (a) and (b) if Skycell months (in thousands of units) to be as shown in Table 8-10. starts with 1,300 employees. What happens to the value of Manufacturing is primarily an assembly operation, and additional overtime as the workforce size decreases? capacity is governed by the number of people on the produc- tion line. The plant operates 20 days a month, eight hours d. Consider part (a) for the case in which Skycell aims for a each day. Production of a router takes 20 minutes, and level production schedule such that the quantity produced production of a switch requires 10 minutes of worker time. each month does not exceed the average demand over the Each worker is paid $10 per hour with a 50 percent premium next 12 months (1,241,667) by 50,000 units. Thus, month- for any overtime. The plant currently has 6,300 employees. ly production including overtime should be no more than Overtime is limited to 20 hours per employee per month. 1,291,667. What would be the cost of this level production The plant currently maintains 100,000 routers and 50,000 schedule? What is the value of overtime flexibility? switches in inventory. The cost of holding a router in inven- tory is $2 per month, and the cost of holding a switch in 2. Reconsider the Skycell data in Exercise 1. Assume that the inventory is $1 per month. The holding cost arises because plant has 1,250 employees and a no-layoff policy. Overtime is products are paid for by the customer at existing market limited to 20 hours per employee per month. A third party has rates when purchased. Thus, if FlexMan produces early and offered to produce cell phones as needed at a cost of $26 per unit (this includes component costs of $20 per unit). Table 8-10 Demand Forecast for FlexMan a. What is the average per unit of in-house production Month Router Demand Switch Demand (including inventory holding and overtime cost) if the third party is not used? January 1,800 1,600 February 1,600 1,400 b. How should Skycell use the third party? How does March 2,600 1,500 your answer change if the third party offers a price of April 2,500 2,000 $25 per unit? May 1,500 June 800 c. Should Skycell use the third party if the per unit cost is $28? July 1,800 900 d. Why would Skycell use the third party even when the August 1,200 700 September 1,400 800 per-unit cost of the third party is higher than the average October 2,500 1,400 per-unit cost (including inventory holding and overtime) November 2,800 1,700 for in-house production? December 1,000 800 1,000 900 3. Reconsider the Skycell data in Exercise 1. Assume that the plant has 1,250 employees and a no-layoff policy. Overtime is limited to at most 20 hours per employee per month. Also assume no subcontracting option. Skycell has a team of

holds in inventory, the company recovers less given the Chapter 8 • Aggregate Planning in a Supply Chain 231 rapidly dropping component prices. per router and $4 per switch. Assume all other data as in a. Assuming no backlogs, no subcontracting, no layoffs, and Exercise 4 except that hiring and layoffs are allowed as in no new hires, what is the optimum production schedule Exercise 5. for FlexMan? What is the annual cost of this schedule? What inventories does the optimal production schedule a. How should FlexMan use the third party if new employ- build? Does this seem reasonable? ees provide only 50 percent productivity for the first two months? b. Is there any value for management to negotiate an increase of allowed overtime per employee per month from 20 b. How should FlexMan use the third party if new employ- hours to 40? What variables are affected by this change? ees are able to achieve full productivity right away? c. Reconsider parts (a) and (b) if FlexMan starts with only c. Why does the use of the third party change with the 5,900 employees. Reconsider parts (a) and (b) if FlexMan productivity of new employees? starts with 6,700 employees. What happens to the value of additional overtime as the workforce size decreases? 7. Return to the FlexMan data in Exercise 4. The company has signed a service-level agreement with its customers 5. Reconsider the FlexMan data from Exercise 4. The firm is and committed to carry safety inventory from one month to considering the option of changing workforce size with de- the next that equals at least 15 percent of the following mand. The cost of hiring a new employee is $700 and the cost month’s demand. Thus, FlexMan is committed to carrying of a layoff is $1,000. It takes an employee two months to over at least 0.15 * 1,800,000 = 270,000 routers and reach full production capacity. During those two months, a 0.15 * 1,600,000 = 240,000 in inventory from December new employee provides only 50 percent productivity. to January. Anticipating a similar demand pattern next year, FlexMan aims to end the year with 6,300 employees. a. Assuming no backlogs, no subcontracting, no layoffs, and no new hires, what is the optimum production a. What is the optimal production, hiring, and layoff sched- schedule for FlexMan? What is the annual cost of this ule? What is the cost of such a schedule? schedule? b. If FlexMan could improve its training so that new employees b. How much does the service contract mandating minimum achieve full productivity right away, how much improvement inventories increase costs for FlexMan? in annual cost would the company see? How is the hiring and layoff policy during the year affected by this change? c. What would be the increase in cost if FlexMan agreed to a 15 percent minimum for switches but only a 5 percent 6. FlexMan has identified a third party that is willing to produce minimum for routers? What would be the increase in cost routers and switches as needed. The third party will charge $6 if FlexMan agreed to only a 5 percent minimum for switches but a 15 percent minimum for routers? Which of the two is better for FlexMan? Bibliography Bitran, G.R., and A. Hax. “Disaggregation and Resource Nahmias, Steven. Production & Operations Analysis 6th ed. New Allocation Using Convex Knapsack Problems with Bounded York: McGraw-Hill/Irwin, 2009. Variables” Management Science 27 (1981): 431–441. Jacobs, F. Robert, Richard B. Chase, and Nicholas J. Aquilano. Operations and Supply Management, 12th ed. New York: McGraw-Hill/Irwin, 2009. CASE STUDY Specialty Packaging Corporation, Part B Julie Williams, facility production planning manager at SPC Specialty Packaging Corporation (SPC), left the meeting with the collaborative forecast team with forecasts and From the discussion of this case in Chapter 7, recall that error estimates for the next three years. She then needed SPC processes polystyrene resin into recyclable/disposable to determine how to meet this demand. Because SPC containers for the food industry. Polystyrene is purchased sometimes outsourced warehousing to its supply chain as a commodity in the form of resin pellets. The resin is partners, one decision Julie had to make was whether to unloaded from bulk rail containers or overland trailers into use public or private warehousing. She also had to de- storage silos. Making the food containers is a two-step cide how much warehouse space to lease or build if she process. In the first step, resin is conveyed to an extruder, chose to use private warehousing. which turns pellets into a polystyrene sheet that is wound (continued)

232 Chapter 8 • Aggregate Planning in a Supply Chain (continued) Table 8-11 Demand Forecast for Clear and Black Plastic Containers Year Quarter Black Plastic Forecast (’000 lb) Clear Plastic Forecast (’000 lb) 2010 I 6,650 7,462 2011 II 4,576 18,250 2012 III 6,293 IV 13,777 8,894 I 7,509 4,064 II 5,149 8,349 III 7,056 20,355 IV 15,399 9,891 I 8,367 4,507 II 5,721 9,235 III 7,819 22,461 IV 17,021 10,889 MAD = 608 4,950 MAD = 786 into rolls. The plastic comes in two forms—clear and black. Overtime is paid at 150 percent of regular-time salary. The rolls are then either used immediately to make contain- Workers are limited to 60 overtime hours per quarter. ers or put into storage. In the second step, the rolls are loaded onto thermoforming presses, which form the sheet Extruders are fairly expensive, and the addition of into container cavities and trim the cavities from the sheet. an extruder requires the hiring of six additional people. These manufacturing steps are shown in Figure 7-11. SPC Each new extruder incurs a fixed cost of $80,000 per currently operates for 63 working days each quarter. Each quarter. Any new personnel hired need to be trained. work day consists of eight hours of regular time and any Training cost per person is $3,000. As a result, SPC has scheduled overtime. decided not to purchase any new extruders over the current planning horizon. During any quarter, available Demand Forecast for Next Three Years extruders may be idled if they are not to be used. The only savings here is the salary of associated workers. The collaborative forecasting team used the historical Laying off each worker, however, costs $2,500. If idled demand data provided in Table 7-4 supplemented with extruders are brought online, SPC incurs a training cost stockout data to develop a forecast for quarterly de- of $3,000 per worker. mand for both clear and black plastic containers. The demand forecast between 2010 and 2012 is shown in Thermoforming Presses Table 8-11. The plant currently has 25 thermoforming presses. Each Extruders thermoforming press requires one operator and can produce containers at the rate of 2,000 pounds per hour. The extrusion process is capital intensive, as is the invest- SPC pays each operator $15 per hour including benefits. ment in the facilities required to support it. The plant Overtime is paid at 150 percent of regular-time salary. currently has 14 extruders. Each extruder has a rated Workers are limited to 60 hours of overtime per quarter. processing capacity of 3,000 pounds per hour. A Presses may be idled for the quarter if they are not to be changeover is required whenever the extruder switches used. Laying off a thermoforming operator costs $2,500, between clear and black sheets. SPC estimates that there and training a newly hired operator costs $3,000. is a 5 percent capacity loss due to changeovers. The effective processing capacity of an extruder is thus 2,850 Subcontracting pounds per hour. Each extruder requires six workers. SPC pays each worker $15 per hour including benefits. SPC has the option of subcontracting the production of plastic sheets to one of its supply chain partners; sufficient

Chapter 8 • Aggregate Planning in a Supply Chain 233 capacity is always available on the open market. SPC Private warehousing also results in operating spends $60 per 1,000 pounds of plastic sheet produced by costs, both variable and fixed. Private warehousing is a subcontractor. available from a third-party logistics provider who has agreed to charge SPC a variable operating cost Materials Management Practices of $4 per 1,000 pounds of plastic sheet stored per quarter. To obtain this rate, SPC must sign a lease for Resin purchased is stored in silos. As there is no short- the full three years. As a result, SPC will pay for the age of resin in the market, it can easily be purchased at space each quarter even if it is not used for storage. $10 per 1,000 pounds when needed. As a result, SPC’s SPC must take this cost into account when making practice has been to purchase resin on a quarterly basis its decision. to match the planned production. SPC must consider several variables in determin- As the extruders produce rolls of plastic sheet, the ing the amount of warehouse space it requires. Usable amount required at the thermoforming presses is passed warehousing space is the fraction of a warehouse that can forward, with the rest driven via shuttle trailer to one of actually be used to store inventory. Considerations are two public warehouses. Transportation is again required made for aisle space, shipping and receiving dock space, to bring the sheets back from the warehouse when they administrative office space, and ceiling height. Storage are needed to feed the thermoforming presses. SPC’s density is another consideration. SPC must also take total transportation cost is $2 per 1,000 pounds of plastic into account velocity and times of materials movement sheet. Each quarter, SPC follows a policy of first using because the staffing level required and storage configura- sheets in storage for thermoforming and only then using tions are dependent on both. For example, if materials the newly produced sheets. Any sheets left over at the must be retrieved readily, the warehouse layout must end of the quarter are put back into storage. This policy include a greater ratio of aisle and staging space to actual is followed to ensure that sheets do not deteriorate storage space. because of time in storage. The Actions and Decisions Public Warehousing Julie and her group must take two actions. The first, Public warehousing charges customers for both material given a three-year forecast as shown in Table 8-11, is to handling and storage. The SPC plant contracts with local come up with an aggregate production plan. The second warehouses to store material on a per-thousand-pound is to choose from the following three options: basis. Material handling charges are from $4 to $6 per 1,000 pounds unloaded at the warehouse. Storage 1. Continue with the strategy of storing materials charges are from $10 to $12 per 1,000 pounds in storage off-site in public warehousing. at the end of each quarter. The SPC plant negotiates annually with local warehouses to establish rates for 2. Lease and run a private warehouse to handle off-site each cost element. inventory. Private Warehousing 3. Use a combination of both public and private warehousing. Operating a private warehouse requires capitalized investment either to construct a facility or to lease an In the case of private warehousing, Julie must existing facility. Lease rates in any location are deter- make a decision regarding the square footage to be mined by the economics associated with building costs leased. This decision will apply over the period 2010 to in that location and the option value of a lease versus a 2012. Clearly, this decision must be made in conjunction long-term capital commitment. Leases are typically in with the preparation of an aggregate plan over the three- force for three years, but the time span can be shorter year period. Ideally, the two decisions should be made depending on a given company’s negotiating strengths. jointly, as each will affect the other. Several viable leasing options exist for the SPC plant, all more favorable than the option of building a new facility. What factors do you think influence the actions Lease rates average $4 per square foot per quarter in and decisions? For example, do you think that the price each location. On average, one square foot is required the subcontractor charges has any relationship to the per 1,000 pounds in storage. amount of private warehousing space to be leased? Julie also has to decide how to handle any potential error in the demand forecast. How do you recommend she handle these errors?

9 {{{ Sales and Operations Planning: Planning Supply and Demand in a Supply Chain LEARNING OBJECTIVES After reading this chapter, you will be able to 1. Manage supply to improve synchronization in a supply chain in the face of predictable variability. 2. Manage demand to improve synchronization in a supply chain in the face of predictable variability. 3. Use sales and operations planning to maximize profitability when faced with predictable variability in a supply chain. In Chapter 8, we discussed how companies manage supply by using aggregate planning to make optimal trade- offs in a way that maximizes profits. In this chapter, we build on the knowledge we gained from Chapter 8 and continue to expand our scope beyond the enterprise to the supply chain as we deal with predictable variability of demand. We also discuss how demand may be managed to counter predictable variability through the use of price and promotion. By managing supply and demand together, managers can maximize overall profitability of a supply chain. 9.1 RESPONDING TO PREDICTABLE VARIABILITY IN THE SUPPLY CHAIN In Chapter 8, we discussed how companies use aggregate planning to determine supply to maximize profits. Demand for many products changes frequently from period to period, often because of a predictable influence. These influences include seasonal factors that affect products (e.g., lawn mowers and ski jackets), as well as nonseasonal factors (e.g., promotions or product adoption rates) that may cause large, predictable increases or declines in sales. Predictable variability is change in demand that can be forecasted. Products that undergo this type of change in demand create numerous problems in the supply chain, ranging from high levels of stockouts during peak demand periods to high levels of excess inventory during periods of low demand. These problems in- crease the costs and decrease the responsiveness of the supply chain. Supply and demand management through sales and operations planning (S&OP) can significantly improve performance when applied to predictably variable products. 234

Chapter 9 • Sales and Operations Planning 235 Faced with predictable variability, a company’s goal is to respond in a manner that balances supply with demand to maximize profitability. The goal of sales and operations planning is to appropriately combine two broad options to handle predictable variability: 1. Manage supply using capacity, inventory, subcontracting, and backlogs. 2. Manage demand using short-term price discounts and promotions. The use of these tools enables the supply chain to increase profitability, because supply and demand are matched in a more coordinated fashion. To illustrate some of the issues involved, let us consider the garden equipment manufacturer discussed in Chapter 8, Red Tomato Tools. Demand for garden tools is seasonal, with sales concen- trated in the spring. Red Tomato must plan how it will meet the demand to maximize profit. One way requires Red Tomato to carry enough manufacturing capacity to meet demand from production in any period. The advantage of this approach is that Red Tomato incurs low inventory costs because no inventory is carried from period to period. The disadvantage, however, is that much of the expensive capacity is unused during most months, when demand is lower. Another approach to meeting demand is to build up inventory during the off-season to keep pro- duction stable year round. The advantage of this approach lies in the fact that Red Tomato can get by with a lower capacity, less expensive factory. High inventory carrying costs, however, make this alter- native expensive. A third approach is for Red Tomato to work with its retail partners in the supply chain to offer a price promotion before the spring months, during periods of low demand. This promotion shifts some of the spring demand forward into a slow period, thereby spreading demand more evenly throughout the year and reducing the seasonal surge. Such a demand pattern is less expensive to supply. Red Tomato needs to decide which alternative maximizes its profitability through its S&OP process. Often companies divide the task of supply and demand management into different functions. Sales typically manages demand, while operations manages supply. At a higher level, supply chains suffer from this phenomenon as well, with retailers managing demand independently and manufacturers managing supply independently. Lack of coordination hurts supply chain profits when supply and demand management decisions are made independently. Therefore, supply chain partners must work together across enterprises to coordinate these decisions and maximize profitability. The S&OP process facilitates such coordination. We illustrate the value of this coordi- nation through further discussion of Red Tomato. First, we focus on actions that a supply chain can take to improve profitability by managing supply. 9.2 MANAGING SUPPLY A firm can vary supply of product by controlling a combination of the following two factors: 1. Production capacity 2. Inventory The objective is to maximize profit, which, for our discussion, is the difference between revenue generated from sales and the total cost associated with material, capacity, and inventory. In general, companies use a combination of varying capacity and inventory to manage supply. In the following sections, we list some specific approaches to managing capacity and inventory with the goal of maximizing profits. Managing Capacity In managing capacity to meet predictable variability, firms use a combination of the following approaches: • Time flexibility from workforce: In this approach, a firm uses flexible work hours by the workforce to manage capacity to better meet demand. In many instances, plants do not

236 Chapter 9 • Sales and Operations Planning operate continually and are left idle during portions of the day or week. Therefore, spare plant capacity exists in the form of hours when the plant is not operational. For example, many plants do not run three shifts, so the existing workforce could work overtime during peak periods to produce more to meet demand. The overtime is varied to match the fluctuation in demand. This system allows production from the plant to match demand from customers more closely. If demand fluctuates by day of the week or week of the month and the workforce is willing to be flexible, a firm can schedule the workforce so that the available capacity matches demand better. In such settings, use of a part-time workforce can further increase capacity flexibility by enabling the firm to put more people to work during peak periods. Telemarketing centers and banks use part-time workers extensively to match supply and demand better. • Use of seasonal workforce: In this approach, a firm uses a temporary workforce during the peak season to increase capacity to match demand. The tourism industry often uses seasonal workers. A base of full-time employees exists, and more are hired only for the peak season. Toyota regularly uses a seasonal workforce in Japan to match supply and demand better. This approach, however, may be hard to sustain if the labor market is tight. • Use of subcontracting: In this approach, a firm subcontracts peak production so that internal production remains level and can be done cheaply. With the subcontractor handling the peaks, the company is able to build a relatively inflexible but low-cost facility in which production rates are kept relatively constant (other than variations from the use of overtime). Peaks are subcontracted out to facilities that are more flexible. A key here is the availability of relatively flexible subcontractor capacity. The subcontractor can often provide flexibility at a lower cost by pooling the fluctuations in demand across different manufacturers. Thus, the flex- ible subcontractor capacity must have both volume (fluctuating demand from a manufacturer) as well as variety flexibility (demand from several manufacturers) to be sustainable. For example, most power companies do not have the capacity to supply their customers with all the electricity demanded on peak days. They instead rely on being able to purchase power from suppliers and subcontractors who have excess electricity. This allows the power companies to maintain a level supply and, consequently, a lower cost. • Use of dual facilities—specialized and flexible: In this approach, a firm builds both specialized and flexible facilities. Specialized facilities produce a relatively stable output of products over time in an efficient manner. Flexible facilities produce a widely varying volume and variety of products but at a higher unit cost. For instance, a PC components manufacturer might have specialized facilities for each type of circuit board as well as a flexible facility that can manufacture all types of circuit boards. Each specialized facility can produce at a relatively steady rate, with fluctuations being absorbed by the flexible facility. • Designing product flexibility into the production processes: In this approach, a firm has flexible production lines whose production rate can easily be varied. Production is then changed to match demand. Hino Trucks in Japan has several production lines for different prod- uct families. The production lines are designed so that changing the number of workers on a line can vary the production rate. As long as variation of demand across different product lines is complementary (i.e., when one goes up, the other tends to go down), the capacity on each line can be varied by moving the workforce from one line to another. Of course, this requires that the workforce be multiskilled and able to adapt easily to being moved from line to line. Production flexibility can also be achieved if the production machinery is flexible and can be changed easily from producing one product to producing another. This approach is effective only if the overall demand across all the products is relatively constant. Several firms that produce products with seasonal demand try to exploit this approach by carrying a portfolio of products that have peak demand seasons distributed over the year. A classic example is that of a lawn mower man- ufacturer that also manufactures snowblowers to maintain a steady demand on its factory throughout the year. In the services field, an example comes from strategy consulting firms,

Chapter 9 • Sales and Operations Planning 237 which often offer a balanced product portfolio, with growth strategies emphasized when eco- nomic times are good and cost-cutting projects emphasized when times are bad. Managing Inventory When managing inventory to meet predictable variability, firms use a combination of the follow- ing approaches: • Using common components across multiple products: In this approach, a firm designs common components to be used in multiple products. The total demand of these com- ponents is relatively stable, even though each product displays predictable variability. The use of a common engine for both lawn mowers and snowblowers allows for engine demand to be relatively stable even though lawn mower and snowblower demand fluctuates over the year. Therefore, the part of the supply chain that produces components can easily synchronize supply with demand, and a relatively low inventory of parts has to be built up. Similarly, in a consult- ing firm, many of the same consultants produce growth strategies when they are in demand and cost-reduction strategies when these are in demand. • Build inventory of high-demand or predictable-demand products: When most of the products a firm produces have the same peak demand season, the previous approach is not feasible. In such an environment, it is best for the firm to build products that have more pre- dictable demand during the off-season, because there is less to be learned about their demand by waiting. Production of more uncertain items should take place closer to the selling season, when demand is more predictable. Consider a manufacturer of winter jackets that produces jackets both for retail sale and for the Boston Police and Fire Departments. Demand for the Boston Police and Fire jackets is more predictable, and these jackets can be made in the off-season and stocked up until winter. The retail jacket’s demand, however, will likely be better known closer to the time when it is sold, because fashion trends can change quickly. Therefore, the manufacturer should produce the retail jackets close to the peak season, when demand is easier to predict. This strategy helps the supply chain synchronize supply and demand better. Next we consider actions a supply chain can take to improve profitability by managing demand. 9.3 MANAGING DEMAND Supply chains can influence demand by using pricing and other forms of promotion. Promotion decisions are often made by retailers without taking into account the impact on the rest of the supply chain. In this section, our goal is to show how supply chain members can collaborate on pricing and aggregate planning (both demand and supply management) decisions to maximize supply chain profitability. Let us return to Red Tomato Tools, the garden equipment manufacturer. Green Thumb Gardens is a large retail chain that has signed an exclusive contract to sell all products made by Red Tomato Tools. Demand for garden tools peaks in the spring months of March and April as gardeners prepare to begin planting. In planning, the goal of both firms should be to maximize supply chain profits because this outcome leaves them more money to share. For profit maximization to take place, Red Tomato and Green Thumb need to devise a way to collaborate and, just as important, determine a way to split the supply chain profits. Determining how these profits will be allocated to different members of the supply chain is key to successful collaboration. Red Tomato and Green Thumb are exploring how the timing of retail promotions affects profitability. Are they in a better position if they offer the price promotion during the peak period of demand or during a low-demand period? Green Thumb’s vice president of sales favors a promotion during the peak period because this increases revenue by the largest amount.